Noob NGINX / self-host question

Hi all. Noob question/s here. I want to be able to access my Immich server (docker) externally and maybe set up some others (e.g. Mealio). My understanding is that I need (should) use NGINX reverse proxy for this. My questions are:

1. Do I need to set up NGINX on a VPS (or similar cloud based server) to send the queries to my home box?

2. Do I need to purchase a domain (randomblahblah.xyz) to use as the main access route from outside my house?

Thanks a lot.