What is the direction of our solar system in the Milky way galaxy and in the whole universe? Are we heading toward another constellation, not including Andromeda?
Pretty much everything in the Milky way orbits around in the same direction. It's a big spinning disk. The Solar System completes and orbit every 200 million years or so. Now, what "direction", other than "the same direction as anything else", I'm not sure there's an answer cause there's no clear frame of reference.
Andromeda and the Milky Way should collide in about 4 billion years, or 20 orbits or so from now.
As to whether we're heading for another collision, well, probably, but none as exciting as the Andromeda one cause Andromeda's much bigger. There's a number of dwarf galaxies in our local group and many of them a lot closer to us than Andromeda.
We may actually be in the process of a collision with a dwarf galaxy, Canis Major. (see article below). http://www.universetoday.com/21914/the-closest-galaxy-to-the-milky-way/
here's a map of the local group (you won't see Canis Major in local group map cause it's already inside the Milky Way.
Sagittarius is the closest dwarf galaxy.