How should I reply to "Dude, are you there?"

English was developed prior to the advent of instantaneous, long-distance, voice communication and so the use of spatial deictics is not so cut and dry. In normal cases, here means "close to the speaker," and there means "close to listener and/or far from both parties," but there are cases in phone conversations where there is more appropriate for a speaker to use in referring to his/her own location. For example, when speaking to someone who has a mistaken idea of your location:

A: You're supposed to be waiting in front of the restaurant.
B: I'm already there, on the north side.

In the Dude, are you there? example, however, I do think that it sounds more appropriate to say Yeah dude, I'm here. Saying I'm there sounds slightly awkward in such a situation, but not nearly as awkward as saying Yes, dude.

Consider also the use now, a temporal deictic, which usually, but doesn't always mean "at the time of speaking/writing."

In phone conversations, here refers to where you are and there refers to where the person you're talking to is.