Why does the white wire on my kymco movie 125 keeps overheating and burning out the alternator . Thanks

check the ground wire, some where not even connected and install a pig tale to the battery to charge it on the scooter, if the wires are OK you need a new stater check with kymcoforum.com and look up bet and lose

Depends how you drive it, but normally you could expect around 40 to 50 Kms per liter.

Not always necessary to change the regulator/rectifier. Check all connections to make sure they are clean, use a good contact cleaner and finish off with dielectric grease on your electrical connections.
When some bikes get a few years on them the connections get dirty. Check to see if there are any burned or discolored wires anywhere around the regulator. The FIX on some bikes is to cut the connector completely out and solder the wires together and either seal them with heat shrink of a good electrical tape. Loose or bad connections get hot. As long as the regulator and rectifier are working there is no need to replace them if the connections are good.
Ride Safely, Ed

fit in a helical, and keep in the same bolt, that should solve your problem