Yes you get one hit point back per HD on a * hour rest unless you are under the care of a healer then you get double that. That also includes complete rest no other activity.
The two doors that have no room behind them is the fake door traps that you have disarmed. IF you wish to search the area beyond the trap you will have to explain how you are going to get over it.
As you explore the cave system you will find no other goblins in the area.
Once we have swept everywhere else, I'll take a pole or spear and use it to deliberately collapse a near portion of the cover over the pit trap so we can confirm the shape, size, and nature of the pit.
Once that's done, assuming there are no surprises discovered in that effort, I'll say, "I think the safe thing would be for one person to cross with a safety line. They hammer in a piton to match one we put in on this side, run a tight rope between. Then the rest of us cross. We'll have to leave Ghost, that or find some other way to help him."
If the pit is short and filled with spikes, I'll instead suggest carefully lowering people down. We remove the spikes and then the entire group, Ghost included, simply walks across and climbs up.
It is a pit trap and it will take about four hours before you have it cleared enough to make it through and up the other side. You get down to the door and find nothing but a few rags and discarded clothes taken from the kids and others they have eaten. The only treasures are in the big room where the final fight took place.
"I'm sure they found this amusing, putting one of their best traps in front of a refuse room. Lets gather up some of the more usable clothing, several of those kids could use them. We can get the clothes out there now, let Allen know of what's going on, and then loot the place thoroughly."
Out of Character: Looks like our precautions on resting up were not necessary, I suspected as much, but better safe than sorry.
Out of Character: You mean the one at the lower right end of the map? That is where we are at now, nothing behind it but clothes and scraps, Kn implied we already explored everywhere else in trying to find more goblins in any case. Nothing left but cleanup.