How to floor the loft without compressing the insulation

For occassional storage chipboard or any plywood 1/2" or greater will be fine. Go to 5/8 minimum if your joists are on 2' centers.

I personally don't agree with the advice to use plywood. Chipboard is fine: it's strong, and it's made using waste materials so it's more ecologically sound to use it where it's appropriate. It's not appropriate for applications that are exposed to the elements in any way: in those cases plywood is more durable so justifies the 2x cost and the extra environmental impact.

Chipboard does have a strength axis, which you might as well take advantage of it: you want the joists running across the short side, i.e. 5 joists on every 4x8 sheet if the joists are on 2' centers.

Chipboard made for flooring has a tongue-and-groove along the long side. That's because while the short sides are supported by the joists, the long sides bridge the joists. Locking a tongue into a groove prevents sagging between the floor joists. Obviously not a big deal for you storage loft, but if it only costs a few more bucks for the tongue-and-groove I'd get that. I've only seen that in 3/4" and 1", BTW, so if you get that you'll have a proper floor up there that you could hold a neighborhood dance on.

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.