Learn English – ‘All week, all the time, all day’ time markers

Yes, these can make sense.

What did you do this week?

You wouldn't generally expect people to say "What did you do this week?" on a Monday morning. But if you are speaking with someone on a Friday night--or a Saturday or Sunday--the mention of "this week" in the past generally refers to the "work week" (Monday thru Friday).

But it could also be used with something recurring, where the recurring thing being discussed has finished...but you are still "in the same week" to refer to it as "this week".

Imagine you are taking a class that has a session every Wednesday. You could say "I just finished class" and someone could ask "What did you do this week?"--meaning "What happened during your class in this week's session?"

I finished my homework this week.

Imagine that you had not finished your homework for one of those classes you have sessions for once a week.

Now it is the next class. As you hand your homework in, you might tell the teacher "I finished my homework this week!" (to say you did a better job...this time).

The argument isn't between broke and had broken, but between broke and has broken. Broke and had broken don't even belong to the same time frame. This is basic sequence of tenses.

You would say:

Mike had already broken his mother's vase when she walked in.

Or, in this case:

Mike broke his mother's vase last night but he hasn't told her yet.