Slip is not enough rudder for the selected angle of bank. If you were in a 30deg turn to the right and the ball on your turn co-ordinator was to the right, it is telling you there isn't enough rudder (yaw) to balance the turn.
This is slipping.
A Side Slip is as you said, cross controlled.
e.g. right roll, left rudder giving not enough rudder or yaw to balance the turn. But you are not intending to turn, that is why you use oppostite rudder and maintain a heading (forward slip due to a forward reference).
You can side slip in a turn to really get down, thus no longer a forward slip, just a side slipping turn.
A Skid is the opposite.....too much yaw or rudder input. Don't get slow and do this.
Crab is an angle the nose is offset with wings level. If you were approaching a runway with a cross wind, you would crab the nose into wind to allow you to track the extended centreline. Keep this crab on during the flare and as you get your first sink, hold off with the usual back pressure and start to straighten the nose. As you do this, the secondary effect being roll, apply a small amount of opposite aileron to prevent the roll. Keep this on and start applying more and more. This will keep the centre line as you touch down and during braking.
Landing like that is a bit risky due to the blanking and gust/mechanical turb. that may happen. In short, you can stall the tailplane and stress the flaps. He may be able to feel a problem before it happens, but cessna's can bite.