Wiring a transformer with two primary windings
First of all your diagram is showing 2 separate transformers. If it is one transformer there should be only one magnetic core like in picture below. There is no 2 primary winding transformer model in CircuitLab. So if you really need it you should create it.


A)"What is the proper way to wire such a transformer?"
You can wire in any order. Good practice is to wire all winding in same direction to avoid phase reversal.

B) "If I decide to make S1 and S2 center-tapped, will I have to use P2 as well?"
No. Just leave P2 ends not connected.