Yes, the battery should be charging while the engine is running, although some of us have had better luck than others. I'm still using both of the original batteries in my atv's, and they're from 2007 and 2008.
It totally pays to use a battery tender, rather than a trickle charger. I picked up two on the weekend at Harbor Freight for $5.00 each.
It sounds like we have the same parking brake device. Mine is a vertical pin that is pushed when the lever is pulled in fully. I lubricated both cables with Maxima Chain Wax, and adjusted the drums so they were equal and not dragging. They work great.