Thought / Meditation

What is thought's role in meditation?

Meditation (the state and not a particular technique or practice) is the absence of thought from its habitual position as a perceptual filter or arbiter. Thought occurs, but it is relegated to a role where it does not dominate consciousness, but rather is one of the many events encompassed by consciousness.

Can one meditate while they are performing other tasks like doing the dishes, driving, or working?

"One" never meditates, meditation occurs. This can happen during an intentional practice or at other times, including "doing the dishes, driving, or working." There is no direct cause-and-effect relationship between intentional "meditation" practice and the actual state of meditation, the best any practice can do is to perhaps (nothing is vouchsafed!) "prepare the ground," that is to at most encourage conducive conditions for the onset of the meditative state.

Is it possible to meditate the entire time you are awake?

Yes, but if you are keeping track that is not meditation. :-)

What role does thought play, if any, in meditation?

Thought of course is the author of intent and therefore the parent of any intentional meditation practice, but in the actual meditative state thought is but one of an infinitude of events encompassed by consciousness -- it does its rightful task of labeling and storing perceptions as experience transparently and does not occlude or coopt in-the-moment awareness.