Yes, you can charge the battery on or off the bike. The battery to bike connection is the same as the bike to charger connection so the same charger charges the battery on or off the bike. the battery removal process is 2 fiddly little torx screws with non captive bushings put through from the inside on the tabbed battery cover, and then a slick and quick and easy 1 retained bolt arrangement for holding the actual battery in place.
I have mine connected with garmin so the battery percentage and human power output show on my display while riding, but there is also a yamaha app that will tell you the precise percent charge on your phone. Both a bit awkward to setup (the first time, you have to do a button dance to put the bike in a mode where it will connect, which it remembers forever).