I cannot recommend this optic for an airgun as ATN makes no mention of these units being air rifle rated. But if you choose too use it, yes it will require an IR illuminator to get a good image and whether you will need an additional battery will depend on how long you will be using the unit, but battery life should be approximately 8-12 hours.
Yes, this should be fine for your muzzleloader.
These specific optics are only rated up to a .308, so no it is not recommended for a 7mm.
While you don't need the batteries in the unit, I would probably leave them in the optic in case you have a momentary connection issue with the battery pack
This ATN X-Sight II Day/Night Vision Smart HD Technology Rifle Scope is no longer available. I would recommend the ATN OPMOD X-Sight 4K Pro 3-14x Smart Ultra HD Day/Night Hunting Rifle Scope, which can handle the recoil of 300 Win Mag and has a ballistic calculator that is compatible with 300 Win Mag. You can find it by using the link below:
https://www.opticsplanet.com/opmod-x-sight-4k-pro-3-14x-smart-ultra-hd-day-night-hunting-rifle-scope.html
I cannot speak to the durability on a Scar, but because of the large reciprocating mass in the unit, I personally wouldn't attempt it.
This is ATN's contact information:
CONTACT INFORMATION
1341 San Mateo Avenue South
San Francisco, CA 94080
Phones: 650-989-5100, 305-900-6841
Office Open: Mo-Fr 7:00am to 4:30pm PST
info@atncorp.com
I would not recommend it as the recoil rating from ATN is .308. You would be much better off going with the X-Sight 4K models as those are rated for higher calibers.
Digital night vision almost always required some form of ambient light, so without an illuminator you would be relying on the conditions of the night. I would say between 50-100 yards is probably the type of range you will get out of the unit depending on the conditions of the night.
The batteries included are not rechargeable batteries. These units run off of standard AA batteries, but can also use Micro USB battery packs.