Thanks @ MimroRaMero

For part 2: For employment work as as TA, I had received an I-9 card from the university. I think you are right that it may not involve any USCIS process. I will stick with "NO".

Part 3: It makes sense that we are applying for EAD under TPS and that category should be right.

Regarding the photos I think they should be recent ones. What do you suggest is a good place for a cheap and quick pp photos?

Thanks much,