Is it possible to use umod to give everyone in the admin group the same F1 abilities as if you typed moderatorid on them? I feel like it is awkward to have to do oxide.usergroup add to each admin and then having to do moderatorid on every person again.

Players that are "owner" in Rust are automatically added to the "admin" group in Oxide. This could be done for moderators too via a plugin, if you made one to handle that. Being in a group in Oxide though will not give them ANY permissions automatically, only the permissions from plugins that you grant that group access to.

So if you want "moderators", you'd have to add them to the desired group and then use plugins such as Secure Admin, Enhanced Ban System, etc. to give them permissions like they would have in Rust.

How do I give people the ability to use the F1 menu though? And how do I assign someone to a group temporarily on connect so I can store the groups in a mysql database instead of a json file?

You'd have to utilize a plugin such as Give if you don't want to add them as moderator in Rust.

A plugin like have to be made for your other task.

Does that plugin allow F1 to work? It seems to only allow giving by typing /give. And also what about allowing f2 to work?

Yes, it does both.