Personal pronouns in the dative case, yes.

So, are "mir" and "dir" dative pronouns?

The rough equivalent in English is "to whom" or "for whom". Certain verbs go with the dative, for example "Der Lehrer hilft den Schülern" is literally "The teacher helps TO the students". That is, we say "help someone" but in German you word it as "help to someone".