Isn't "Я теж їсти хочу" also grammatically correct?
It is, and it's usage is not SO seldom to claim that it's not added just not to confuse the learners. I added it, now it's accepted, thanks!
Thank you, can you maybe also update a few other questions that are similar to these?
Uh. Well, I found one more and updated. Maybe there are more, but I don't see them for now.
I thought position didn't matter in Ukrainian. I put "Я хочу теж їсти" and got it wrong. Why?
Not any word order sounds natural. Some do make one sound like Yoda :) E.g. "Я їсти хочу теж" sounds weird as well.
I would say this one sounds awkward and unnatural because of the placement of теж, between хочу and їсти.