Who is correct: me or my teacher?

First of all, guys, I'm sorry if this is the wrong place ou se eu deveria postar a pergunta em português. Eu fiz a mesma pergunta para uma comunidade americana e aproveitei-a nesse post. Entrei e conheci o fórum, de fato, a pouquíssimo tempo. Voltando:

...so I received this test, corrected by my high school english teacher. I'm pretty sure that she is wrong on the correction of some answers, but she wouldn't discuss it with me, saying things like "oh, what can I do, it's not portuguese!". I didn't argued with her because I wanted to ask someone else before saying something wrong.

One of my answers was: ...she was studying and eating that day. (or something like that). My teacher said that I should put another "she" before the verb "eating", so it would be "she was studying and she was eating that day". And I'm sure my answer is correct. What you think?

The second one was a question: "Could you help me in this question?" (or something like that, again) and there were two possible answers below: "Yes, I'm going to help you" OR "Yes, I'll help you". Now I notice how "I will" seems to be more appropriated, but I also think that "I'm going to" isn't wrong. It's a certain action (even if decided in the moment of speaking) and the use of "going to" is also accepted. Isn't it?

Those are some of the questions I remember from the test. Could some teacher or more experienced english speaker help me, please? I'll try to get the other ones later (she took our tests).

Thanks a lot!