This will easily handle the recoil of an AR10. Since it is an AR platform, you would need an extra high mount such as this: https://www.opticsplanet.com/vortex-cantilever-ring-mount-for-1-inch-tube.html
We recommend medium height rings.
If mounted in quality rings at proper torque, yes!
The throw lever at the link below should work with the Vortex Crossfire II 4-12x44mm 1in Tube Second Focal Plane Rifle Scope.
https://www.opticsplanet.com/switchview-eagle-eye-universal-scope-magnification-adjustment-throw-lever.html
The power-range is indeed 4x on the low end, and 12x on the high end! This is an outstanding magnification range for most hunting scenarios, overall. Magnification as high as 18x is often preferable to precision target shooting and varmint hunting, otherwise!
The Monstrum extended series 30mm cantilever mount is designed for AR pattern rifles in order to provide the proper centerline height. Which may be too high for a Ruger 10/22. I would recommend using medium height scope rings like the TRYBE Optics Advanced Scope Rings, found by using the link below:
https://www.opticsplanet.com/trybe-optics-advanced-scope-rings.html?_iv_tube-diameter=1-in&_iv_ring-height=medium
To mount the Vortex Crossfire II 4-12x44mm Rifle Scope to a Henry .22LR I recommend using the Leupold RM Rimfire No Tap Ring Mount for Scopes w/ 1in Tubes. I recommend using the medium or high rings for that set up. These rings can be found at the link below.
https://www.opticsplanet.com/leupold-22-rimfire-no-tap-ring-mounts.html?_iv_ring-height=3-sl-8-in
The Bergara BMR comes with a 30MOA Rail so if I am not mistaken you would just need rings. The 1" diameter medium height Vortex Pro Series Rifle Scope Rings at the link below should work for that set up.
https://www.opticsplanet.com/vortex-pro-series-30mm-riflescope-rings.html?_iv_tube-diameter=1-in&_iv_ring-height=medium-0-dot-95-in
The Vortex Crossfire II 4-12x44mm Rifle Scope would work well on a Mossberg 22LR Rifle. I would also consider the Leupold VX-Freedom 3-9x40mm Rifle Scope with the Rimfire reticle which can be found at the link below.
https://www.opticsplanet.com/v/174181-leupold-vx-freedom-rimfire-3-9x40.html
I would recommend the Vortex Pro Series Riflescope Rings, the 1 inch medium height rings. You can them here:
https://www.opticsplanet.com/vortex-pro-series-30mm-riflescope-rings.html?_iv_code=VX-RR-VRPRR30-PR1-M