No, that wouldn't work because it doesn't correct the preposition at the end of the sentence.

7. I’ve been knocking on this door for ten minutes: why didn’t you let me in?

Correction: why didn’t you open it. (not sure how else to change it)

8. This little puppy has been appearing at our door every day for the past week, and we are not sure who it belongs to.

Correction: we are not sure to whom it belongs.

I'm not sure about the first one, but the second one would be:

This little puppy has been appearing at our door every day for the past week, BUT we are not sure who it belongs to.