1. Does not the QRH say fire the bottle if the handle is still red after fuel to cutoff? It is not a given, but conditional.
2. Testing the Fire system after completing the QRH is hardly going against the QRH. You have done as told, but then, for your own comfort, done a little extra which would appear not to effect any other system.
3. What I was taught, and pass on with enthusiasm, is "QRH complete" check Recall. There may have been a multiple failure and there are other issues to be addressed. It also tells you the status of the a/c and will help in the review phase of what to do next. "QRH complete" does not end the thinking process, but sadly that is what many seem to think. The classic is "no crew action required", only to find at the next landing the MEL grounds the a/c. Oops; the QRH says nothing about checking MEL in flight, but the C.P. will think it bad captaincy if you park the a/c at the wrong airfield and they have to spend mega bucks getting it home.
There is much the QRH doesn't tell us. It needs to be used with intelligence and common sense and airmanship.