I wrote a bit of rude reply on my son's English test!

[LinoleumBlownapart]

Now I'm feeling a bit bad and I can't erase it because I wrote in pen, but my son got 8.75 out of 10 on his English as a second language test (we live abroad) but he chose the only right answer and the teacher marked it wrong. I wrote because I thought maybe she wanted the answer in past perfect! On the second page he got another question wrong, I think she wanted him to write "haven't" but he wrote "don't have". But "My parents haven't a lot of money" sounds wrong, but is it? I'm attaching pictures because I'm confusing myself. AIBU to talk to the teacher or should I let it go and not be one of those parents.

“My parents haven’t had a lot of money” sounds odd on its own to me.

I might use it if I were to say something like “My parents haven’t had a lot of money since the lawsuit” or “My parents haven’t had a lot of money, so the lottery win will really help.”

She sounds a bit awkward!

Well you are right about 'chose' being the only correct option so she's made a mistake there. On the other section of the test though it is asking him to use the present perfect so the correct answer would be 'haven't had' (don't have/haven't - are present simple) so the teacher is right to mark it wrong.
Half unreasonable/half not

PolkadotsAndMoonbeams my son added the "this" because he's a numpty (again I think rushing to finish and go outside to play football). It should read "She hasn't been studying all morning", he is sure he saw the word 'this' and thought she wanted "She hasn't been studying all this morning" so he added the -'at'. I have a personal pet hate for these re-arranged sentences, they often take me a while to figure them out, so I can't see how that benefits anyone who is actually learning the language. But that's neither here nor there.

Your son chose the correct answer. None of the other answers are grammatically correct unless you change 'have chosen' into 'had chosen' like you did. I don't think it's rude. The teacher might feel offended if they are the type who don't like to be corrected. As for the first image, I couldn't see it properly.

The team had chosen the name of the team at the beginning of the season sounds correct to me. It sounds past tense so I would have used had not have. Have is in the present tense.

I suppose that could be correct given the choices on the paper but it’s not the way I would have worded that sentence. If it was referring to a present tense situation I would have worded the sentence as, They have chosen the name of the team as it is the beginning of the season. No need to mention ‘the team’ twice in the one sentence. That makes it feel clumsy.