Battery tender won't hurt, but if your charging system is in good shape and you are riding the bike regularly, it's not strictly necessary. I don't use them on my bikes, which get ridden maybe once a week during the winter.
I would definitely use a fuel stabilizer. In my experience, Stabil and Seafoam work equally well to stabilize fuel. Seafoam has made a noticeable difference in smoothing out slightly rough running on a bike that's been sitting for a while.
Whatever you use, make sure it's run all the way through the fuel system.
Also, if the bike sits for more than a few weeks without running, you should drain the carbs.
You couldn't hear a dump truck driving through a nitro glycerin plant!
Badasses might screw with another badass. Nobody screws with a nut job.