For the rear indicator staying on, check out and clean your earths it may help it may not.
The number plate lights, what are the contacts in the bulb holders like? the contacts to the bulb may be corroded. also maybe check the bulbs on a battery.
the side light, check the earth coming in from the light and the connection for the actual indicator circuit.
A cheapo mulitimeter and a workshop manual are worth their weight in gold for niggling electical problems in my opinion.