There's a "Communities" button at the top of the page (or in the top menu on mobile) that shows all communities on your current instance.
I'm not sure for your search question. It looks like they tried to implement that function in the general search tool (magnifier icon at the top/menu), but filtering by a specific community doesn't seem to work for me. There are still some bugs to work out on the site in general.
I'm not sure I understand. But the search option in the top right is useful for almost everything. If you're looking for communities you can use browse.feddit.de and paste them into the search to sub to them. You can reply if you have any issues
I'm new as well, you can search by clicking the magnifying glass at the top right of your screen, next to the notifications button and your username.
I'd insert an image here, but the new lemmy update has broken image uploading.
That's not quite how all of this works yet AFAIK. This isn't exactly what you're looking for, but he's a directory of migrated Reddit communities: https://sub.rehab/