There is currently not a sunshade available for the Burris Fullfield E1 6.5-20x50mm 1in Tube Second Focal Plane Scope.
Yes, Burris scopes are rated for 50 BMG recoil energy.
To mount the Burris Fullfield E1 6.5-20x50 mm Rifle Scope to an AR I recommend using a 1" diameter cantilever mount. The mount at the link below should work.
https://www.opticsplanet.com/warne-quick-detach-gen-2-extended-skeletonized-msr-mount.html?_iv_tube-diameter=1-in
The Burris Fullfield E1 6.5-20x50 mm Rifle Scope is resistant to a lifetime of field use, heavy recoil, and harsh vibration. However, the holdovers are designed specifically for .22-250 rounds, and are mil-based. So the holdovers will not translate to 30-06, but it should handle the recoil fine with a proper ring and base setup.
The turrets are capped.
This can hold up to it. But you would need to purchase rings for this scope. Would need to be 1 inch tube and high height for rings.
This would be a good scope for 300 win mag and can withstand the recoil.
The holdovers are designed specifically for .22-250 rounds, and are mil-based.
This works well with .243 Win and you would need high rings for that rifle.
It would work well for a 6.5 Creedmoor rifle, and a 1 piece mount like the one linked below would be a good option:
www.opticsplanet.com/burris-ar-tactical-mounts.html?_iv_tube-diameter=1-in