It's better to buy a cleaning fluid for lens filter. 

The camea can take 1.6v rechargeable batteries, but in general rechargeable battery might drop its voltage quick depend on its physical performance. In the cold weather, recommend using Energize lithium batteries to get longer lifetime. 

I don't see why not, remember that the filter goes on the lens, not on the camera. 

I've never used Hoya ND's, but I have GOBE, KERNEL, ZOMEI, and K&F ND filters. Out of all of them, I like the K&F the most because the colors look great out of the camera and they don't create a vignette around the edges like some of my other nd's which I hate. Because of the great out of camera colors, it gives you more to work with on post-production when you shoot on a flat profile. Also, I've used them during night photography on bulb mode to do light painting and the 4 - 6 stop ones work great for this. Overall, I think for the money the K&F filters are worth it. Awesome product! 

This filter will fit any lens with a 49mm filter thread