Tasco states this sight is recoil tested to withstand the recoil of a rifle, but does not specify an exact caliber rating; .223/5.56 rifles fall well within normal rifle recoil levels, so it should hold up fine on those platforms.
This sight uses a single CR2032 battery, which is included with the unit and can be replaced with any standard CR2032 coin cell.
The Tasco Pro Point 1x30mm 5 MOA Red Dot Sight can be used on a crossbow, however, it does not use any crossbow specific adjustments. It will fit 3/8-inch tip-off and 5/8-inch Weaver-style bases.
Per the manufacture: "Recoil tested to withstand the recoil of a rifle." They do not specify the maximum caliber that this optic will be able to withstand.
Yes, this will be compatible with the 3/8" grooved receiver of the Henry AR-7.
https://tasco.com/content/Manuals/RED%20DOT%20SIGHTS/TRDPCC_ProPoint_RedDotSight_FullManual_5LIM_web.pdf and here is warranty information https://tasco.com/customer-service/
This is compatible with weaver rails, which will also fit most picatinny rails, like what is on an AR15.