cdb,
I assume you are talking about the UK PAOM Pt1 CAP 612?
You will have to give me a bit more of a clue to some of your questions, if you want answers. Are your references page numbers or paragraphs?
In general, the PAOM Pt1 is an appallingly structured document full of inconsistency and contradictions. As you say, it also contains stuff that every pilot should know and that tends to go out of date too. It needs a complete re-write which is threatened soon apparently.
In effect it is a document that is jointly agreed between the Home Office and the CAA, but the CAA is the lead.
The question about snipers is outside my expertise but I understand there is considerable doubt as to their accuracy. If it really became necessary, I suspect that a military sniper and aircraft would be used anyway.
Police aircraft have no special clearance or right to enter zones. They gain clearances just the same way as everyone else by making a request to ATC. If you are referring to an incident in an ATZ without an ATC controller, then no one needs a clearance into such airspace. Police aircraft can operate with a higher priority than other aircraft, but they still need a clearance.
Flying single pilot, you pretty much have to remember immediate actions, if you are to do them immediately.
"Perf" does not relate to the aircraft it relates to the performance group that the pilot chooses or has to to adopt. All current UK police aircraft are twin engine and Cat A, but sometimes some of them can operate Perf Gp B by operating at a mass greater than permitted for Perf Gp A. There were some singles in the early days, but largely because they cannot be used at night they have disappeared.