It seems you are missing some very basic knowledge, if you have questions like this. Watch/read some tutorials to get the basics, than ask specific questions.

This guy does the same thing as you: https://www.youtube.com/watch?v=yLduQiQXorc

This was like the 3rd result for searching for nginxproxymanager on yt.

You type the ip of the rpi on the router, so from an external call the router will forward it to the rpi. Or I don’t know what is your question.

Things may seem automagical in the networking scene, but you can config anything the way you want. Even in nginxproxymanager you can edit the underlying actual nginx configs with their full power. The automagic is just the default setting.

External 80 to internal 80 and external 443 to internal 443

With this config you don’t have to deal with ports later, as http is 80, https is 443 by default.

If you run some container on port 81, you have to deal with that in the reverse proxy, not in the router. E.g. redirect something.domian.tld to 192.168.0.103:81

If you use docker check out nginxproxymanager, it has a very beginner friendly admin webui. You shouldn’t forward the admin ui’s port, you need to access it only from your lan.