What's your favourite F-Droid app?

Termux, definitely Termux. Best terminal emulator for Android.
It basically gives your phone as much power as you can get from a locked down system.

You can even install GUI in it. I use XFCE. Pretty useful for Handbrake as I am too dumb for ffmpeg, Firefox (desktop) because it won't crash with huge uploads to e.g.: OneDrive like every mobile web browser when you lock your phone, NOAA-APT to decode APT imagery from NOAA 15, 18 and 19 satellites.

Just some examples from what I use it for:

ping
traceroute
telnet/ssh client
wget for serious downloads and poor man website mirroring
tar for creating archives
gpg for encrypting files
gzip for compressing files
touch for modifying timestamps
Vim for text editing (yes, I know)
rsync for backups (if not using tar)

Now it gets even better

socat for port forwarding
VNC Server (tigervnc) for accessing the Termux GUI
SSH Server (OpenSSH) for remote CLI access and secure port forwarding
NGINX server for serving the websites you mirrored with wget and as a forward proxy for other web-related services (to get them on same port, add basic authentication, use HTTPS,...). I also use it for serving videos in a lazy way (checkout fancyindex module).
kiwix-serve for serving archives from kiwix.org. I have (not only) the whole motherfucking English Wikipedia on my phone (110GB)!
Navidrome server to stream music locally stored on my phone (currently 1,339 songs at ~23GB) with a nice web-ui. Also supports adding internet radios.
Jellyfin server (under Ubuntu proot) if you have some movies too. I ditched this idea, but I tried it, and it works.
cloudflared for creating Cloudflare tunnels to perhaps access this from internet (if you feel OK about that). You can test it by creating quick tunnel which doesn't even require account (limited to HTTP).
HTTP proxy server (tinyproxy) to use my phone for internet access (will also route it over VPN). If your carrier restricts hotspot usage, this is the way. For me it's useful to circumvent blocking on school network without the need for any extra software on school PCs.

You get the idea. Plenty of stuff to do with it.
You can also run these distros under proot with proot-distro easily:
Alpine, Arch, Artix, Debian, Deepin, Fedora, Manjaro, OpenKylin, OpenSUSE, Pardus, Ubuntu, Void.

Oh, now for a warning. Things like NGINX save error logs to your storage by default. Sometimes (e.g.: your phone disconnected from Wi-Fi making an active interface disappear and logs being firehosed) they can rapidly fill it up. INTERNAL STORAGE FULL TO THE LAST BYTE MAY CAUSE A BOOTLOOP!!! (Guess how I know)

In my case forcing it to reboot into recovery, shutting it down, and booting it up manually (instead of auto reboot after system crash) did the trick, freeing 17MB, enough to boot up.

I have used Termux, even have it installed right now but apart from the odd cron job, I never used it for something heavy. You, sir, are basically running full fledged Linux with it.
you can install firefox desktop with termux? how?
- First you need to set up GUI: https://wiki.termux.com/wiki/Graphical_Environment
  You could also use Firefox without WM or DE, but it's not nice.
  
  Since you already enabled the x11-repo in this step, you can just pkg install firefox.
  
  VNC Client: https://github.com/bk138/multivnc
It sounds absolutely and completely overpowered for a phone... ... Well, what did I expect ¯\_(ツ)_/¯

How bad is the battery drain?

Depends on what I do with it. Usually the only noticeable drain is WiFi being active.

But for example encrypting and compressing large files will absolutely toast the phone.

The errors can be a problem, even if they aren't written to a file. For example with tinyproxy. Disconnecting the network interface it's running on won't shut it down, it just keeps producing errors and clearly doing something as it can really heat up the phone.
This is what it spits out (as fast as it can):

...
ERROR     May 25 13:01:06.107 [9701]: Accept returned an error (Invalid argument) ... retrying.
ERROR     May 25 13:01:06.107 [9701]: Accept returned an error (Invalid argument) ... retrying.
ERROR     May 25 13:01:06.107 [9701]: Accept returned an error (Invalid argument) ... retrying.
ERROR     May 25 13:01:06.107 [9701]: Accept returned an error (Invalid argument) ... retrying.
ERROR     May 25 13:01:06.112 [9701]: Accept returned an error (Invalid argument) ... retrying.
ERROR     May 25 13:01:06.112 [9701]: Accept returned an error (Invalid argument) ... retrying.
ERROR     May 25 13:01:06.112 [9701]: Accept returned an error (Invalid argument) ... retrying.
ERROR     May 25 13:01:06.112 [9701]: Accept returned an error (Invalid argument) ... retrying.
ERROR     May 25 13:01:06.112 [9701]: Accept returned an error (Invalid argument) ... retrying.
ERROR     May 25 13:01:06.112 [9701]: Accept returned an error (Invalid argument) ... retrying.
ERROR     May 25 13:01:06.114 [9701]: Accept returned an error (Invalid argument) ... retrying.
ERROR     May 25 13:01:06.114 [9701]: Accept returned an error (Invalid argument) ... retrying.
ERROR     May 25 13:01:06.114 [9701]: Accept returned an error (Invalid argument) ... retrying.
ERROR     May 25 13:01:06.114 [9701]: Accept returned an error (Invalid argument) ... retrying.
ERROR     May 25 13:01:06.114 [9701]: Accept returned an error (Invalid argument) ... retrying.
ERROR     May 25 13:01:06.114 [9701]: Accept returned an error (Invalid argument) ... retrying.
...

Which is also why I run it with -d which keeps it in foreground and this goes to stdout/stderr instead of a file. I keep everything I can in foreground. I can have multiple sessions open and just CTRL-C anything.

I have an RTLSDR any good beginner friendly apps for it? Ive used a pi for NOAA before and it worked really well with SATNOGs. Being on the go with it would be fun.
- SDR++ is great for both desktop and Android: https://github.com/AlexandreRouma/SDRPlusPlus
  
  Unfortunately, it's sometimes a bit buggy, but it's by far the best there is. Well, these are nightly builds, so I guess it's expected.
  
  There's also SatDump which has many decoders, including NOAA APT and Meteor LRPT: https://www.satdump.org/download/

Tubular. It's a fork of newpipe incorporating sponsorblock and youtube dislike.

This doesn't show when i search for it on F-Droid 🤔
- It's in IzzyOnDroid repo
I like pipepipe cause it lets you see comment chains instead of just the top one
- Tubular does this now too
It is honestly better than YouTube Premium. Watt Google should offer as part of its paid suite, an open source software does it.

i like breezy weather as a weather app
binary eye for scanning qr codes
aegis authenticator to replace google authenticator
adaway to block ads on certain apps, not perfect but better than nothing

I reccomend Rethink DNS instead of Adaway. Might be overkill, but you can just disable those features.

I had to uninstall Vector Pinball because it was TOO favorite. Like, the motion sensor lights in the bathroom at work would shut off.

Fuck. Why are you telling us about it?

I should have never installed it, damn it
- Lol! It's so good though! I'm sure I'll have another fling with it before long.

Nobody seems to mention Rethink DNS.

Seems greatly overlooked. Previously I used InviziblePro, RethinkDNS is much superior. I can't imagine Android without it.

Customizable DNS blocking, firewall, great logging, Wireguard and Orbot integration. Even GrapheneOS recommends it for a DNS block.
It's really a great app and has replaced AdAway for me completely.

Just because somebody might now the answer here: Sometimes the DNS is offline but I do not notice that have no internet connection. Only later I notice I had "No internet" the whole day. Anybody knows if there is a way to enable a notification when that happens? Not sure if I explained correctly.
DNS + firewall + VPN

Oooohhh, that's a lot in one app. My suspicions are raised...

Fossify Gallery: https://f-droid.org/packages/org.fossify.gallery/

I've only really dipped my toes in F Droid but getting back Simple Gallery minus the recent changes has been well worth it.

Simple suite of apps used to be good until the dev sold it to some company, I think. The versions on F Droid are still clean, but on Play Store, they are riddled with ads until you pay, I think.
- Yeah, agreed, that's what I mean. I use Fossify now, but the apps are basically identical, without the crap.
In the same vein, fossify notes is so incredibly nice after years is notepad apps being riddled with bullshit!

Organic Maps (google maps replacement) - https://f-droid.org/packages/app.organicmaps/

AntennaPod (podcast app) - https://f-droid.org/packages/de.danoeh.antennapod/

Everyone knows the popular ones so here's a shout out to a few that are perhaps not so commonly known:

whoBIRD - Shazam for birds
Subz - Subscription manager
zCard - Loyalty/membership/store card wallet

My most used can no longer live without app:

Joplin - Note taking. Various sync options. Brilliant app, helpful community & very regular updates (especially desktop)

Jerboa!

I got it from the regular play store and I'm on it right now. Is it any different from F-droid?
- It's just as free as it is independent on F-droid

These are probably the ones I use the most

Just as a heads up, the simple apps got bought out. The foss versions go by fossify now https://f-droid.org/packages/org.fossify.messages/
- Thank you, for the heads up :)
Owntracks link is broken.
- Weird! It works on my end :-S

Fennec, a flavour of Firefox that strangely consumes much less battery than the official Firefox app.

My favorite ones are:

Bura as a weather app
LinkSheet to choose which apps to open links in
HeliBoard as a keyboard

Plus one to LinkSheet. I haven't used the others though.
For me its omweather for weather. But the best thing about open source is we can chose.

I just started using Local Send (https://f-droid.org/packages/org.localsend.localsend_app/) ; what a blessing this app is, no more uploading to ~~someone else's computer~~ the cloud and downloading to my pc or vice versa, it's so fast too

Binary eye. The best damn QR (and other codes) scanner there is.

It's also on the play store but I don't care I just like it a lot.

'Russian links doesn't work"..

Cannot download..

Unexpected Keyboard or Super Tux Kart tough choice

oh wow, unexpected keyboard is amazing for termux/Linux
I hadn't heard of Super Tux Kart so I just went and tried it out and man...it seems awesome but the control schemes are all so incredibly awful. Do you know if there's controller support?
- I have no clue, but hope at least a DS4 would work
  
  edit: someone on yt has been able to wire up an xinput controller, so there's something at least

FairEmail. I got fed up with the Gmail app injecting ads despite I pay for storage and services. FairEmail is not beautiful by modern standards but with some tweaking I can live with it, no problem.

Thumb-key, mull browser, keepassdx, kiss launcher, tuta mail, ntfy

Runner up (running tracker)

Breezy Weather

Shizuku, Symphony for playing local music (jellyfin for streaming), and most of all Termux. Without Termux I wouldn't be able to use some CLI-only stuff on the go, use neovim, or SSH into my server to perform some quick task.

Hold up; is Jan 11, 2022 really seriously the last time Temux was updated anywhere? Wtf?
- https://github.com/termux/termux-app/issues/3848

Loyalty card keychain - copy bar codes in to load up and scan, can create shortcuts to specific ones, cranks screen brightness while a code is open

Kotatsu - manga reader

OsmAnd for obvious reasons.

Breezy weather, cause goddamn is it nice to have an actually good weather app that doesn't want the most bullshit permissions that a weather app shouldn't ever need access to.

Image Toolbox - it's pretty nice.

Cool Reader - dead project, it's successor KnownReader isn't on F-droid, but it doesn't matter much. I still haven't gotten completely used to known, cool works perfectly fine and it has been my e-reader of choice ever since the j2me days.