the 'Prime' position is normally with the fuel tap lever pointing straight down. 'Reserve' is with lever pointing forward, and 'On' with lever pointing back. Check which position the fuel flows when engine isn't running. Have you checked the workings of the actual fuel tap itself ? These vacumn taps have 2 hoses from the rear, a large one which runs down to the carbs, and a smaller one which fits on to the inlety manifold. Check these lines, make sure they aren't split or loose. They have to be tight and in good condition.
Check the rubber diaphragm inside the fuel tap. If this is split, it won't pull fuel from the tank. The bike may still run OK on 'prime' position, but no good on the other 2. If this is the case, the diaphragm is rooted.
To check your battery, the simple test is to start the bike and turn the headlight on. Give the bike a rev - does the headlight get a bit brighter ? If it does, the battery and charging system is working. If you have a multitester, run the leads across the battery terminals. At idle, the voltage should be around 12v DC. Any less, the battery is on the way out. Give the bike a rev, the battery voltage should rise to around 13.5 volts, it may go as high as 14. Any higher than 14 then the regulator is on the way out.
These are just simple tests, sometimes you need to dig a lot further into testing alternator leads, rectifier outputs etc, to track down electrical problems.
Coil resistance needs to be checked against the relevant specs in the workshop manual.