Would Rather (Sooner) vs Would Prefer 3

ANSWERS 1: PREFERS DOGS TO
Prefer is used to say what you prefer in general.
Prefer + noun + to + noun
Common Errors:
She prefers cats than dogs. X
She prefers cats to dogs. V

ANSWERS 2: YOU DIDN'T SMOKE | YOU DID NOT SMOKE
Would rather is the same as would sooner. Would rather + she, you etc + past simple (present/future) expresses that we would like someone else to do something.
Common Errors:
She prefers cats than dogs. X
She prefers cats to dogs. V

ANSWERS 3: SOONER WE DIDN'T BUY | SOONER WE DID NOT BUY
Would sooner is the same as would rather. Would sooner + she, you etc + past simple (present/future) expresses that we would like someone else to do something.
Common Errors:
I would rather you not go to the party tonight. X
I would rather you didn't go to the party tonight. V

ANSWERS 4: PREFER TO PLAY FOOTBALL RATHER
Would prefer is used to say what somebody wants in a particular situation (not in general).
Would prefer to do something + rather than + (do) something.
Common Errors:
She would prefer go to the party rather than stay at home. X
She would prefer to go to the party rather than stay at home. V

ANSWERS 5: IT IF YOU DIDN'T | IT IF YOU DID NOT
Would prefer + it + if is used as a part of a second conditional. Note that would prefer in this type of sentence has an object "it".
Would prefer + it + if + she, you etc. + past simple (present/future).
Common Errors:
I would prefer you didn't drink so much. X
I would prefer it if you didn't drink so much. V

ANSWERS 6: PUBS TO STAYING
We use prefer + ing to say what you prefer in general.
Prefer doing sth + to + doing sth.
Common Errors:
He prefers fishing than jogging. X
He prefers fishing to jogging. V

ANSWERS 7: NOT TO TALK
Would prefer is used to say what somebody wants in a particular situation (not in general).
Would prefer not to do something (in the negative form).
Common Errors:
She would prefer not go to the party. X
She would prefer not to go to the party.V

ANSWERS 8: RATHER NOT DANCE
Would rather is the same as would sooner. It is followed by an infinitive without to.
Would rather not do something (in the negative form).
Common Errors:
I wouldn't rather go to Scotland. X
I would rather not go to Scotland. V