Grimrock

I've fired the serpent staff and opened the door. I threw a rock onto the pressure plate and that opened the door. I can't get past that

The you have to open the door with the staff and press the little button beside the grate where the fireball hits

Then you must step into the teleporter on you side. You will be teleported to the actual position of the moving one. From there shoot open the door press the plate. The grate to the powergem shpould open. In an other teleporterjup, jump to the place before the grate and go to the gem and continue from there

The grate to the power is open. Now what. If I go into the teleporter on the south side, it transports me to the north side. But all the pits are open and I can't get to the power gem and further. The moving teleporter on the north side moves me back to the south side. When I fail, I fall into the pit and I get a message in the upper left hand corner "ignoring teleportation, party falling to level below"
What do you mean by "jump to the place before the grate".

The two teleporters are connected. When you step into the one, you're teleported to the other. There are, I believe, 2 safe points that you can teleport to. One is when the teleporter is over the place in front of the power gem. The other is in that alcove to the right, where the teleporter kinda "disappears" to before beginning the cycle again.

Stand adjacent to the teleporter on your side, and watch where the other one goes. When you know the other teleporter is going to move to a safe spot, step in. You've gotta get your timing right. "Jump to the place before the grate" means step in to your teleporter right before the other one moves over the space you want to land on. The teleporter moves kinda fast, so if you wait until it's over the place you want it to be before you move in to your portal, you'll miss and wind up in the pit.