There are two bodies, and Gate would work.
Astral Projection:
"You and up to eight willing creatures within range project your astral bodies into the Astral Plane.... Your astral from is a separate incarnation.... If a creature's original body or its astral form drops to 0 hit points, the spell ends for that creature." PHB 215 (emphasis added by me)
From the spell description we can conclude that a creature under the effect of Astral Projection has two separate corporeal forms located on two separate planes. Essentially, they are split into two separate creatures sharing a single consciousness.
Gate:
"When you cast this spell, you can speak the name of a specific creature. If that creature is on a plane other than the one you are on, the portal opens in the named creature's immediate vicinity and draws the creature through it to the nearest unoccupied space on your side of the portal." PHB 244 (emphasis added by me)
As a reminder, a creature affected by Astral Projection is both on their original plane when having cast the spell, and on the Astral Plane. Therefore, if you are casting Gate from the original plane targeting a creature affected by Astral Plane, they do count as being "on a plane other than the one you are on" as defined by the Gate spell.
What would happen is their astral body would be pulled through the Gate to your plane (a plane other than the Astral Plane). Then, as per the Astral Projection spell:
"If you enter a new plane or return to the plane you were on when casting this spell, your body and possessions are transported along the silver cord, allowing you to re-enter your body as you enter the new plane." PHB 215
As far as other spells...
Consider which body would be effected by that spell, if not both of them. Each spell would need to be considered individually and the outcome should be determined by your best judgement.
In the case of Sending, I suspect the message would reach both bodies (given the 5% chance to not reach the astral body), but would not be heard by the unconscious physical body.
In the case of Scrying, you would end up reaching the unconscious physical body should the spell succeed.
Yes, you can.
The part of the scrying spell description about targeting a location says:
Instead of targeting a creature, you can choose a location you have seen before as the target of this spell. When you do, the sensor appears at that location and doesn't move.
It doesn't specify that you must have seen the location physically; any form of "sight" is enough. It's a concentration spell, so you can't have multiple castings of scrying active at the same time, but you don't need to - you just need to have seen it at some earlier point. And per the earlier portion of the spell description:
You can see and hear through the sensor as if you were there. [...] A creature that can see invisible objects sees the sensor as a luminous orb about the size of your fist.
As such, from a straightforward reading of the spell, you can indeed choose a location you have previously seen through the scrying sensor as the target for a new scrying spell.
The spell description doesn't specify how closely you must have seen the location, or how specific the location you choose must be. As such, this is something that's left to the DM to adjudicate.
Best Answer
Scrying is limited to targets on the same plane
The part of the scrying spell that lets you target a location says that you target a location "instead of targeting a creature". This indicates that unless otherwise noted, any the restrictions on which creatures you can target also apply to scrying on locations – the only thing that changes is the type of the target. This means that the requirement for the target to be on the same plane of existence applies to all valid targets for the spell.