1) Wrong fucking forum. Read the rest of the forums and the other forum descriptions before actually posting. Lurking is also advised.
2)Use the pipboy to rest(press p, or look at the right bottom of your interface and find a pip-button). And go leave the cave. Healing up isn't necessary, at least not in the beginning, since you are automatically partially healed while travelling.
3) You can only get back into the vault after you've left the cave at least once. They don't want you to come running back with a "the real world is scary"-routine.