50 mm Yongnuo lens filter size is 58mm, you can reconfirm your lens mark as "ø" (diameter) symbol, if the number is 58mm, it would be ok ,thanks. 

Yes, I believe you can with any trail cam. There are several videos on YouTube. You need a 4.0x1.7mm plug. I saw one video that explains a direct hard wire. After watching some videos, I decided it was easier and about the same price to buy the Stealth Cam 12v external battery pack with solar panel. I paid $50 at Academy Sports online. Plus the 4.0x1.7mm plug from Amazon. But if you like to make things, there are plenty of videos on making your own solar battery packs. 

Yes, it is threaded on both sides (male and female). This is a very high quality filter for the price. 

This will work on any 82mm lens. 

The way u tell is to look at the end of you lens. There will be a 0 with a slash / through it and a number behind it. Match that number to the 58 of this neutral density filter.