I love the solar bullet but use it pretty much with other bullets rather than the one that came with it. So, yes, the remote does work with any jacked bullet - at least all the ones I've tried.
It is about average strength for a bullet. Much stronger, to me, than those watch battery powered mini bullets. Obviously not hitachi level but comparable to most bullets.
You do not need sunlight to charge it. It will charge in the light from a light bulb, too. Just like solar calculators.
You also do not need to have light while using it. Light charges the battery and the battery holds the charge to work for about a half hour to an hour (depending on what strength you use it at and how charged up it was) or so in the dark.