I don't see any inherent differences in meaning. The sentences in which the prepostion takes the object seem more formal and prescriptivist, but I think that's the only real difference.
However (I could be wrong here) but I think
2.1. Whom are you looking for?
is incorrect. Whom is the subject and therefore should be the subjective case (who) - whereas
2.2. For whom are you looking?
presents whom as an object (the object of a preposition) and must be in the objective case (whom).
- For Teachers