Hi Ryonan
Congrats on the pre-GCSE.
The common reply to 1. is "No, I wouldn't mind" which surprisingly isn't even a choice.
Of the choices provided, all of them could work because three of them are ambiguous. My choice, the unambiguous one, B. "No, don't shut it." 1. Would you mind if I shut the window?
A. Yes, (I agree with you. It's cold in here) I would
n't mind (if you did shut the window)
Problem: punctuation
Repair: Yes. I wouldn't mind.
A. Yes, I wouldn't mind.
Problem: Yes is positive,
wouldn't negative.
Repair: Yes, I would mind. Don't shut it.
Repair: No, I wouldn't mine. Please shut it.
B. No, don't shut it.

Here the speaker is not replying to the question "Would you mind" but rather to the act of shutting the window:
Sam: Shut the window?
Max: No, don't shut it.
C. Yes, [I agree with you. It's cold in here] please shut [it].
I added "it". Problem: punctuation
Repair: Yes. Please shut it.
C. Yes, please shut.
Problem: missing object
Repair: Yes. Please shut it.
D. No, [I wouldn't mind] please do.
Problem: punctuation
Repair: No. Please do.
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Speakers might purposely shorten look like (meaning, appearance) to like because of the ambiguity that results. For example, using look like makes Sam appear shallow here:
Max: So, I hooked you up with Pat for this Friday night.
Sam: What's Pat look like?
Max: Are appearances all you care about?
Shortening look like to like helps out because of the ambiguity it houses:full phrase: look like
Default meaning, appearance
Elliptical phrase: (look) like
Default meaning, appearance
Secondary meaning, character
Max: So, I hooked you up with Pat for this Friday night.
Sam: What's Pat like?
Max: He's nice or He's tall, dark and handsome.
In short, like is ambiguous, and because of that A., while it is correct, is not the best answer here:2. What's Alice like?
A. She has long hair.

B. She's very nice.

In other words, A. houses the secondary meaning, appearance, whereas B. houses the primary meaning, character.
Note, the default meaning rules, unless context suggests otherwise. For example, Max and Sam are talking about appearances, and so here like means appearance, not character--but it could if they wanted it to:
Max: I'm hooking up with Robin on Friday. He's good looking, to say the least.
Sam: What about Pat? What's he like?
Max: He's a tall, cool glass of water. Not bad on the eyes.