We use would prefer or 'd prefer, followed by a to-infinitive or a noun, to talk about present and future preferences: I'd prefer to go by myself. Would you prefer a quieter restaurant? She'd prefer not to drive at night.

What is the noun form of prefer?

Noun form of prefer is preference. .

Is would prefer correct?

Prefer and would rather can be used interchangeably. As you indicate, Omar, when we are talking about general preferences, prefer is followed by verb-ing, thus: I prefer listening to music to watching TV. I'd rather listen to music than watch TV.