1. yes.
2. yes.
3. ?
....just my opinion, and I'm sure someone may have another. Sounds like it is a trickle/float charger already. The plug/clips are interchangeable I think, in operation. If your riding once a week, does it even need to be plugged in? I go 2 weeks or more without plugging in...again, just my thoughts. Batteries seem pretty solid these days...a battery tender is about 40 bucks last time I knew.