From Alabama, welcome to the site.
Feb-Oct ~ 12,500 kms must is a good amount of riding and I imagine most was in your cooler season. A new battery may be quite warranted. I've gone through two on my 07 and Im holding a Odessy 625 ready in the waiting for this up coming cold season becasue my second is already showing signs of degradation. The OEM Yuasa batts don't last long with repeated cold soaking. As for why the radiator fan is kicking on so quickly? Ive no help to offer.
I use a water wetter agent, Proline, that has IMHO significantly reduced engine heat by possibly 15 F degrees, or more. Have you an oil temp gage? I relate oil temp reduction to an overall engine heat decrease. Ive seen at least a 15 F reduction in oil temp and the cooling fan doesn't work as often. The cooling fan comes on at 180. Ive not observed my oil temp above 185. Before using Proline water wetter I saw 205 on occassions.