"...the bike will
not start and stay running!!"
I hope the "not" wasn't supposed to be there?
The headlight should be the same as the small automotive headlights that have both the high and low beam that are available at any auto supply store.
These Royal Enfields don't have the most powerful alternators on them so look for a headlight with a low wattage. My 2011 came with a 35/50w bulb although the Indian AVL manual says it can use a 55/60w 12 volt bulb.
Before replacing the bulb, check to see if the light switch is turned off or to the park position.
If the switch will turn the parking/tail light on and off, some prior owner has removed the bypass jumper. (This is good). If he/she did, there is a chance that the headlight switch is not turned on to the 'headlight' position. If the switch doesn't seem to do anything, the "jumper" may still be installed. If it is, when you remove the headlight for replacement you might look to see if there is a wiring bundle with a connector that plugs into a short bundle which plugs into another connector.
The UCE bikes use this method of bypassing the light switch to meet DOT requirements in the US.
By removing the short plugged in section and then connecting the connectors that remain behind, suddenly the light switch will start working.
I'm not sure if the AVL is the same as the UCE but I would bet it is.
As for the rear sprocket, if the teeth aren't chipped or bent it is probably okay.
The rear drive chain is probably the crappy Indian product that all of us have found to be very poor and easily worn out.
With the bike on the center stand the rear chain should move up and down about 2-2 3/8".