Unfortunately only the higher magnification scope, particularly item 200119, has the remote. You can find that version here: https://www.opticsplanet.com/burris-4-16x50mm-eliminator-iii-ballistic-laserscope-riflescope-remote-cable-swi.html
Unfortunately, Burris lists neither a temperature operating range, nor battery life.
Please call 1-888-440-0244, or email customerservice@burrisoptics.com for additional information.
Mark H.
Yes, this can also be used with a 20moa base.
The Eliminator uses a unique mounting system - and no rings at all. You're going to need a 1-piece picatinny base, as from your description of "twist off/on rings with mounts", it sounds like you have the Leupold DD base and rings, and the Eliminator is not compatible.
The Eliminator mounts to any picatinny rail using supplied picatinny clamps. These clamps will come with your scope: all you need to provide is the rail. The mounts need to be torqued to 50 inch-pounds.
Mark H.