Can I move the kitchen to the living room?
There is practically nothing that money can't solve, so the answer to your question "can I move the kitchen" is "sure". But it could get very expensive.

In particular, looking at the floor plan it looks like almost all of your plumbing is on the east side of the apartment. Water pipes are pressurized and could be rerouted almost anywhere (e.g. under the floor, in the ceiling) but the sewer lines could get a little more tricky, since they need to slope down to the exit. Also, you will need a vertical vent going up from your new kitchen and to the exterior, either through a wall or the roof.

Much of the difficulty will be determined by what kind of access you have above and below your unit (if any).