Heh, welcome to high level campaigning where the rules sometimes only sort of vaguely make clear what happens and the GM works overtime deciding how it actually works in his campaign.
Or basically there is no clear RAW response to these questions far as I know.
Big chunk of text to follow:
1) - Imprisonment vs the astral body. I'd say I'm mostly going to agree with Zhangar. It will Imprison your astral body. This probably isn't going to appear to an outside observer to be terrible different from being put into Temporal Stasis. The Astral normally has no "surface", no place you can be "in a small sphere far below the ground." So I would simply place you in suspended animation right there probably in small personal sized sphere where time simply doesn't flow (which given the local Timeless planar trait might be hard to see as different). Meanwhile your corporeal body back on the Prime is also still in suspended animation from your casting Astral Projection. There is no set or specific duration to Astral Projection ... it can continue indefinitely until time and the prime material cease to exist where you are (and maybe beyond if your campaign is a tad unusual). This is where I differ from Zhangar's response as he implies that there is a limit to the duration on Astral Projection (maybe he didn't intend this given the next portion of his post). Far as I can see there is none, you decide when to return to your prime material body and end the spell unless something ends it 'prematurely'.
2) - Imprisonment vs the 'second' corporeal form. Pretty much as above except the planar conditions will likely be different starting with there is more likely a surface that you can be placed far beneath etc..
The Astral Projection spell pretty much assumes the caster is on the Prime Material. Given high level play (as it exists now vs when this spell was first written) this stands a reasonable chance of not being true so one of the first decisions a GM will need to make is does this spell even work if the caster is not on the Prime Material and if that's the case what are the limits if any? For example, the caster is attempting or wants to use Astral Projection from his own private (and well defended) demi-plane does it work and how does it work (silver cords, color pools, etc.)
As for Trap the Soul - works on the target 'spirit' so yes I'd say it'll work on the astral body and the second planar body if its formed. Think it would tend to 'fizzle' if the casters (soulless aka spiritless) body in suspended animation is the target.
Parasitic Soul - 3rd party spell I'm guessing? Without knowing more I'd say see above.
Binding - should work but getting the caster to sit around for a minute might make this pretty near impossible to work regardless.
Temporal Stasis - Works on the traveler, the spirit but not the spiritless body at home.
As a general rule I'd lean towards treating the body of the caster on the Prime (or where ever they were when they cast Astral Projection) as an 'object' as far as spells go while treating the astral body or body formed on another plane as a 'creature' since it currently houses the caster's 'spirit', soul or consciousness.
Lastly I haven't seen or read any of Pathfinder Chronicles: The Great Beyond.
