Would a wormhole be able to move? First, I consider the following as given: All the galaxies, solar systems and planets in the universe travel on a different route at a different velocity through space, mostly moving away from each other.
Now, imagine we would be able to create a wormhole from planet x in solar system y in galaxy z to planet a in solar system b in galaxy c. Since both planets are moving in different directions, I see 2 options how it could work.
1) The wormholes would travel with the planets, constantly changing the spacetime-wrapping.
2) The wormholes would stay at the position they were initially created, which means the planets would move away from them, after they were created. But the spacetime-wrapping would stay the same.
I know most people (me included) think that option 1 is the case. But the following question really made me think, and led me to the question I'm now asking:
If option 1 was the case, what would happen if someone entered the wormhole? Would he keep the velocity of the planet where he entered at the planet he came out, which means he would move away from the target planet? Or would he adopt the velocity of the target-planet? If the latter was the case, would this person notice the slow-down/speed-up/direction-change? Could the person even die?
I'm not a physicist, so I may assume totally wrong concepts. I'm sorry about that.
 A: Wormholes don't just exist by themselves, they have to be created by a form of matter called exotic matter (which almost certainly doesn't exist, but let's gloss over this). To construct a wormhole you need to gather up some exotic matter and arrange it in a particular configuration.
So if the exotic matter is moving the wormhole will move along with it. However you may find that a considerable force is required to move the matter at the two ends of the wormhole because as they move energy will have to be put into the spacetime warping between them.
Re the second question: a wormhole is not like a Star Trek transporter that instantly moves you from one place in space to another. If you pass through a wormhole you would be floating freely$^1$ just like the astronauts in free fall in the International Space station. Falling through the spacetime in a wormhole is no different to falling through the spacetime around the Earth, except that the spacetime in a wormhole has a rather special shape.
Generally speaking, falling freely through spacetime does change your velocity (as measured by someone who is not falling freely). For example, when Felix Baumgartner jumped out of his capsule his speed relative to the ground changed from zero to Mach 1.25. In that case it was the spacetime curvature caused by the mass of the earth that accelerated him. In the case of the wormhole it would be the spacetime curvature caused by whatever exotic matter you used to construct the wormhole.
So when you emerge from the far end of the wormhole your speed will almost certainly be different to the speed you had when you jumped in. Exactly what your speed will be depends on the exact geometry. The speed will make absolutely no difference to you unless there is something in your way, so putting the far end in a closed room would be a bad (and very messy :-) mistake. In any of the more realistic science fiction stories that use wormholes (and remember, this is science fiction we're talking about) the ends of the wormholes are floating in space so anything emerging from them has lots of room to slow down.

$^1$ though there maybe tidal forces
A: 
2) The wormholes would stay at the position they were initially created

That wouldn't make sense: it's meaningless given the principle of relativity. All sublight velocities are equivalent, and every place in spacetime at a later time is a different place. No velocity keeps you in the same place any more than any other.
Also, regardless of what other forces may affect the mouths, gravity is universal, so nothing could prevent you from gravitationally "towing" the mouths to whatever position and velocity you wanted. (As for other forces, if the mouth is stabilized by exotic matter inside some sort of conventional-matter containment structure, you might be able to just push it.)

1) The wormholes would travel with the planets, constantly changing the spacetime-wrapping.

The motion of the mouths in spacetime (the ordinary part of spacetime, I mean) has nothing to do with the shape of the wormhole region connecting the mouths. The behavior of the wormhole depends entirely on the nature of the magic that created and maintains it, but I don't see how it could even notice careful gravitational towing, given the equivalence principle.
(I suppose it's not impossible that our 4D spacetime could be a surface in a higher-dimensional spacetime with an extrinsic shape and extra dynamics, in which case the mouths might have a preferred position and speed, and trying to move them might actually stretch the wormhole. But that would be a dramatic alteration of general relativity and I'd expect it to show up in some way in cosmological data even if there aren't any wormholes.)

If option 1 was the case, what would happen if someone entered the wormhole? Would he keep the velocity of the planet where he entered at the planet he came out, which means he would move away from the target planet? Or would he adopt the velocity of the target-planet?

If you freefall through the wormhole, you'll come out with the velocity you went in with, transported along your path through the wormhole. In the simplest case, the wormhole would be something like the portals in the game Portal, and your speed relative to the exit mouth would equal your speed relative to the entrance mouth. (Also, much as in the game, you could likely accelerate to arbitrary speed by repeatedly passing through the wormhole if the mouths were appropriately arranged. This is just another reason that wormholes seem unlikely to exist in reality.)
Note that "the velocity of the planet where he entered at the planet he came out" is ambiguous, since there's more than one way to transport velocity from one place to another. If the mouths are in relative motion in the non-wormhole part of spacetime, and you enter one mouth at a low speed, you'll come out at a low speed relative to the exit mouth (velocity transported through the wormhole), not at a low speed relative to the entrance mouth (velocity transported the long way around).
