we all take technological process for granted...
Well, if you're able to travel to other stars in a time frame which allows wars, well, you'll absolutely be able to accelerate a ball to 1'000km/s.

What I wanted the say was, that I consider it impossible to wage wars across more then one solar system effectively, so yeah, a civilization that could do that could probably do anything.

I'm sorry that 1000 sounds so trivial compared to 4...
We're talking about primitive prototype rail guns fired on earth (air resistance, gravity, etc.) which reaches a velocity of 4km/s. This is quite amazing, but still not a miracle. So yes, I would argue that in the future it would be possible to accelerate a projectile to a 1'000km/s in a setting which is better for this style of gun.
Although I'm unsure how the gun would survive the shot. (See below for my reason.)your still talking 2.5 km long rails, these guys want to reach 1000 km/s on rails that (realistically) do not extend greater than 15 meters
Actually there would be no need to have such short guns, you can easily build large structures in space (provided you have a cheap method to bring the necessary materials in space). And it's not like the enemy could change it's course fast enough so you don't really need to move your gun around much for aiming.
As for the force:
v(muz)

2DF/m)^.5
v(muz)=Muzzle velocity (Meters/Second)
D=Length of rails (Meters)
F=Force applied (Newtons)
m=Mass of projectile (Kilograms)
F=m*(v(muz))^2/(2D)
F=2'000'000'000N=2MN (huh, quite a lot)
Hmmm, I thought it would exert a lot of force, but I'm quite a bit surprised at how high it is. This would need some truly massive rails to survive a shot.
I have no idea at all, how we could be able to have rails that would survive the force of one shot.
this is one of those great things people continue to miss, the reason that problem doesnt exist on earth is because we always have something to brace ourselves against and to dissipate energy into (shoulder for guns, ocean for ships, ground for turrets etc.) spaceships have no such failsafe so they take the brunt of every blow they fire, thats why they would be far better off with a series of series-firing guns than one big gun, or a battalion firing in parallel.
Actually no. It doesn't really matter for this if a ship is in space or on earth. It would probably even far better in space than on earth.
A battleships that fires a broadside still needs the structural power to absorb the force of the shots. A ship in space would far insofar better as that it hadn't also to compensate the force which prevents it from moving back at the same time (inert water for the ship on earth), while the ship in space would be able to do that and then could use it's thrusters to move back into position.