I guess it depends. I have thought in dreams before; even to the extent of mulling over a philosophical problem that I was probably thinking about the night before, and engaging in interesting dialogue with people (probably after seeing the film "Waking Life" one too many times).

It depends on whether you consider self-awareness as an integral part of thinking. I would agree, and aside from lucid dreaming, I believe it is possible (as it has happened to me) to be self-aware within the dream, but completely unaware of the 'true' reality of my sleeping.

Is time an actual dimension of reality (i.e. does it take on an existence in-itself) or is it merely a relation only definable within the context of events as I believe coberst was talking about? It seems to me that modern science considers time in the latter category. When scientists speak of space-time they're really talking about something that's one in the same; that both are inseparable from the other.

It's impossible to 'experience' time without events or movements. Even if you're able to remove everything beyond your self, even consciousness itself is an event.

One thing worth mentioning is Einstein's contribution that indeed time isn't universally static but relative with motion.