This is a second focal plane scope.
No, rings are not included.
Yes, there should not be an issue.
It would depend on the distances you are shooting at. I don't know your skill with an AR, but you should safely be able to engage coyotes to 300 yards, if not beyond. The 1x magnification would allow for the use of your AR as a defensive rifle at close range, also. I would recommend a riflescope with a BDC (Bullet Drop Compensating) reticle.
If it's going to be a dedicated hunting rifle, I would again recommend a riflescope with a BDC (Bullet Drop Compensating) reticle, and also a 3-9x. The 3-9x is the most popular magnification range for hunting.
Nikon offers a free app and online program called SpotOn that will let you choose your Nikon BDC riflescope, magnification, ammunition from dozens of manufacturers, zero, target distance - even atmospheric conditions - and generate accurate values for the BDC reticle.
Here's an overview of SpotOn:
https://www.nikonsportoptics.com/en/nikon-products/hunting-spoton/index.page
Mark H.