The bike's starter relay and motor operate off of the 12v battery. Everything else electrical on the bike operates off of stator-supplied AC or rectified DC voltage after the engine is running. Put another way, you don't need the 12v battery at all to ride this bike if you're content using the kicker to start it.
The fan temperature switch is easy to bypass with a short wire with 1/4" male spade terminals. I run mine that way full-time in the hot summer months. Whenever the engine runs the fan does too. If you do this and the fan still doesn't run with the engine running then you have another issue such as poor ground connection or a non-operational fan motor.
The issue you describe with the starter motor sounds like low battery voltage, but I see that you say the battery is fully charged. Other possibilities that come to mind include worn or failed brushes in the starter motor or insufficient lubrication of the bendix as suggested below.