Generally, it is not necessary for you to return to your home country. As long as you are under a valid visa you may adjust status in the U.S.
You do not need to return to your home country to adjust your status if you are in the U.S. on a valid status. You may file an I-485 to adjust your status here in the U.S.
Maybe. It depends on the current visa and your actions. If you here on a J visa you may be prevented from adjusting until either going home for 2 years OR getting a waiver BUT only if subject to the 2 year home residency requirement in the first place. IN ADDITION, you must figure out if you have violated status. If you entered as a student and graduated or dropped out or worked without authorization, see a darn good immigration lawyer first. If you entered on a non-immigrant worker visa and worked for someone other than the petitioner (including yourself in MOST cases), see a darn good immigration lawyer first. It's just not that simple.