Medium height rings should be the ideal fitment. We'd suggest our model #24116
No, mounts are sold separately.
Hawke Sport Optics states that their Endurance 30 WA 4-16x50 IR SF LR Dot Rifle Scope is all caliber rated. However, no specifics regarding airgun recoil is listed by the manufacturer. It should be fine with your rifle, but I'd recommend reaching out to Hawke directly for confirmation.
The difference is the reticle, the LR is a universal reticle, the .223/.308 reticle is calibrated specifically for those cartridges.
We would recommend high rings for that. Talley would be ideal if you do not have rail on the rifle: https://www.opticsplanet.com/talley-lightweight-alloy-scope-mounts-for-browning-howa-remington.html?_iv_gun-model=browning-x-bolt&_iv_ring-height=high. If you have weaver or picatinny bases, you can use Hawke rings: https://www.opticsplanet.com/hawke-sport-optics-2pc-match-series-weaver-scope-rings.html?_iv_diameter=30-mm&_iv_ring-height=high
As listed, the weight is 19.7oz and the parallax adjustment range is 15yds to infinity.
Here is a link to the manufacturer's image of the reticle:
https://us.hawkeoptics.com/hawke/reticles/LRC-16x.svg