Can I extend my loft hatch opening?
Your plan sounds fine. 

If it were me, I would likely do the temporary support from beneath (a temporary stud extending from the floor below, intersecting the ceiling at the intersection of B and P).  Either way, I think you will be fine.

A reciprocating saw is the right tool for this job.  It will allow you to cut the nails holding the existing cross member in place.

I'm not sure of your particular situation, but since you are already reframing the opening, you should consider adding a drop-down ladder.  As long as you have the space, this will make the attic much more usable in general.