Will intergalactic space travel and space habitation be possible within the next 1000 years?
The progress of technology is steadily increasing. Who knows, maybe soon, we'd have a propulsion system that would take us to Neptune in a few days or maybe a few months.
Intergalactic travel maybe possible within the 21st century. Astrophysicists have already given ideas, such as the space warping spacecraft (which could allow it to travel faster than light without breaking the laws of physics) but technology is advancing. That is if we don't kill off ourselves within this century. Space habitation is likely, but we'd need to have spacecrafts that can take us further into the cosmos.
Milky Way's neighbor Andromeda is about 2.52 million light years away. Assuming that a spacecraft can travel (like light) at the speed of light, it would take 2520000 years to reach a star system there. If possible within 1000 years, answer is 'yes'.