When I paste a block, the block often appear well away from the mouse pointer.
Each block has its own pivot point, objects like walls appear on the side of a tile instead of the center. This will make it easier to quickly create buildings, not having to manually move walls after placement. Other blocks similarly have different pivot point, like wheels.
When I try to place a block beside another, sometimes that block just enter to the other. Like nothing there.
You can hold ALT when placing a block to make sure it is the same height as the face you're currently pointing at, you can also use G to align it to the face you're pointing at.
If I place a block and rotate with the space key 90 degree all fine, but when I change the axis the block is off.
Not sure what you mean by this, could you try explain it a little differently?