Basically, there are two major rules regarding the use of the dative case:
1. Dative objects
The question wem? ('to/for whom') only applies to dative objects of verbs that allow or require them. Your examples, however, aren't dative objects since they are governed by a preposition.
2. Prepositions
After a preposition, the dative does not answer the question wem, but is mainly a grammatical feature to mark togetherness while enabling free word order. There are, however, prepositions that can be used with different cases, where the case differentiates the meaning as well (e.g., auf dem und auf den). I'll try to illustrate the difference between prepositional phrases requiring the dative and dative objects with the help of your examples:
Seit dem Krieg and nach dem Konzert are adverbial phrases. The dative case is only conditioned by the preposition. The corresponding questions are:
Seit dem Krieg -> Seit wann?
Nach dem Konzert -> Wonach?
Mit [i]hnen could be either an adverbial phrase or a prepositional object:
Ich spiele mit ihnen in einer Mannschaft -> Mit wem/womit? (adverbial phrase to the verb spielen)
Ich spiele mit ihnen ('I trifle/palter with them') -> Mit wem/womit? (prepositional object of the verb mit jmdm./etw. spielen)
Compare that with:
Ich spiele ihnen übel mit -> Wem spiele ich übel mit? (dative object)
Summary
If a (group of) noun(s) in dative is part of a prepositional phrase, the control question includes always the preposition which frames the meaning. The prepositional phrase can either be an adverbial or a prepositional object.
If a (group of) noun(s) in dative stands on its own as prepositional object, it indeed answers the question wem? ('to/for whom').