You can, just like you could do in Markdown. You can use inline TeX and get the right overall format with a template. I haven't actually done this for a paper, but I used Pandoc to typeset a textbook with lots of math and code and it worked well. We could have used org-mode just as easily, but Markdown was already familiar to my non-Emacs-using coauthor. (Hey, we all have our faults!)

Yes, and you can use Pandoc to export to different formats, including Epub, HTML, Docx, etc. You can embed LaTeX and customize in multiple ways using Lua filters for Pandoc. I've found Pandoc to be more powerful than Emacs when it comes to writing documents in Org mode, while Emacs is more powerful when you use Org mode to do literate programming. YMMV

You can, but you might be better off just using AUCTex if you are emacs anyway.

YMMV with use case, obviously.