I want to start adding new enemies with custom mechanics and my own code to my ROM hack, but I have no idea how to get started with ASM hacking, and there are many terms I don’t understand. The only thing I sort of know how to do is implement an ASM template and use the "run make insert" button. Could someone offer some advice or tell me what I should learn first in order to start writing my own code in the game?

It depends what you want to do. I would recommend starting here though https://bookstack.nsmbcentral.net/books/new-super-mario-bros/page/custom-actors. This covers the basics of setting up an actor. If you need help with anything the best place to ask is on the NSMBC discord server. I do not recommended using AI for anything, it does not have enough knowledge on nsmbds to make usable code. The only one that is half capable at debugging is Claude but I still do not recommended using it