1. If my memory is correct it is prohibited to slip a C-172 at full flap.
2. It is prohibited to slip an older C-150 (with 40° flap).
Half correct.
Some models of C172 had an 'Avoid slips with flaps extended' warning on the panel, and in their POH.
I don't recall a similar warning on any model of C150 I have flown.
No explanation was offered in the 172 POH for the warning, but there are two possible explanations.
1. Disruption of the airflow over the tail, causing pitch control difficulty, as suggested by A and C.
2. On poorly maintained/rigged aircraft, it is possible for wear in the flap multi-track system to allow sufficient sideways movement of the flap, during a side-slip, to jam, or restrict the aileron movement.
I have experienced both of the above on both types, and so now I don't side-slip with flaps in either.
I would suggest that Vilters' option a) Is the safest way to loose height steeply in a C172.
As to the questions posed by the OP, I can't improve on the advice given by A and C, except to add that the higher the speed in the side-slip, the more effective it will be.
MJ