I used a different word order. היא מגישה את זה לנו Is this wrong?
No, but it's less natural. You would use it if you wanted to amphasise that she serves us, not them.
I also used a different word order and was marked wrong.
when is it את זה and when is it אותו
If you know exactly what the אותו is (by context of the conversation), then use it. If it is at all ambiguous, then use את זה.