I would say hinder. If we assume that interesting events are distributed equally throughout space (i.e. the universe is uniform) but differ over time (the early universe was obviously different to the current universe) then astronomers currently get to observe a wide range of events throughout both space and time. If events were observed immediately from all distances, then astronomers would only be able to observe current events.
More of a problem: the edge of the observable universe is simply the edge beyond which light hasn't yet reached us. If the universe is flat and infinite (as it currently appears to be) then in a universe with an infinite speed of light there would be no edge to the observable universe. We would see everything, and the whole night sky would shine like the sun. This would seem to be a hindrance.
edit: On the other hand if the universe just wraps around, then... actually I'm not sure what happens, but I guess every ray of light emitted from a star gets absorbed by something, which would still make the Earth (if planets could even exist) far too hot.
Yes. It would be immensely more difficult if we could not look back in time. There would be no microwave background, for example, so no knowledge of the fluctuations in density soon after the Big Bang.
As a comparison, do you think it would be easier for an alien to figure out the life cycle of humans if they could see a few humans at every period of life (like in astronomy) or if they only saw middle-aged humans, but many more of them?
On the other hand, it would be possible to effectively communicate with distant species, who in turn might have existed for a long time and have records of past events.
