PHP in Templates and Template Conditionals

[Yumi]

From what I read, this allows me to use other stuff like {$header} or {$forums} and so on. Is it?

Yes, this will keep all the functionality of MyBB templates.

And also run PHP codes in templates right?

Yes.

But where do I upload this? /inc/plugins/? And then, I upload it.. and.. it's done? Am I ready to use it or do I have to do something else?

After uploading it, you need to activate it in the AdminCP. Then just edit the templates as you wish.