As soon as the 3 VE's grade it while you are still there. They will give you a CSC right then and there. VEC will then send the results of the testing session to the FCC - usually the next morning. Usually takes about a week (often quicker) to appear on the FCC's FRS and hard copy of your license will follow. Testing dates around national holidays often slow things down a little. Be grateful! My Novice license (1960) took three months to get to me and only then could I fire up the rig. When your callsign appears in the FRS, you're legal and can get started exploring the world of amateur radio first hand.
Depending on if the ve mail the paper work or send the paper work
Electronically. Mail generally takes 3 or 4 days then possibly up to a few days to a week to see your call sign
Electronically usually a few days to a week.