About 30 feet 

For the Nikon 7200 you need a filter in the size 67 mm, this also applies to all lenses. 

First, you need to check whether the camera battery is sufficient. When the battery is below 30%, you cannot take pictures at night. You can see the battery in the lower right corner of the camera screen; then format the memory card; find the delay in the menu Take pictures, note that the factory default setting is 30 seconds, but if the animal stays in front of the camera for less than 30 seconds, the picture will not be taken. You can try to set it to 8 seconds, 5 seconds, etc. 

first 30 days is free then I believe it's $7-10 a month 

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.