In the first example, the verb is reflexive (sich kämmen) English uses reflexive verbs too, only not as extensively as German (I enjoyed myself). With reflexive verbs, the subject ( the one who is actually "doing" the action) is the same as the object (recieving the action either directly or indirectly).
Ich kämme mich. In this sentence literally, you are saying in English...I comb myself (which doesn't make much sense in English, but is considered to be good German).
Ich kämme mir die Haare. In this sentence (die Haare) is a direct object because "die Haare" is actually what is being combed. Me (for myself or mir) is indirect because the combing is being done "for me" but the "hair" is what is actually being combed.
In the second sentence..Ich überlege mir, was wir unternehmen können.. You are thinking "to" yourself, not "about" yourself. If you said...Ich überlege mich.. You would basically be saying..I am considering myself"
Let's look at another reflexive verb...sich waschen
Ich wasche mich (I am washing up..."washing myself"
Ich wasche mir die Hände. I am washing (for myself) my hands.
English makes no distinctions between accusative and dative pronouns. However German does. I think that is what makes it so hard for English speakers, plus the frequency of reflexive verbs in German.