IIRC the prohibition only applies with 40 deg of flap set due to the blanketing effect on the tailplane. Those Cessnas with max 30 deg flap don't have the restriction. However don't trust me, look it up in the POH.
ASI's normally underread in a slip, by how much will vary according to installation and the placement of the pitot and static vents.
One explanation is courtesy of Mr Bernoulli. Passing an airflow across the open end of a tube will reduce the pressure of the air in the tube, when you slip the pressure reduces and hence the ASI reading.
A sideslip also leads to the nose dropping. If you don't apply a bit of backward pressure you'll find you come out going faster than you went in. Try it at a safe height, checking the height on entry and exit until you find the attitude that gives you the exit speed you want.