To mount the Vortex Crossfire II AO 6-18x44mm Rifle Scope to a Bergara BXR I recommend using medium height rings. The Vortex Pro Series Rifle Scope Rings located at the link below will work.
https://www.opticsplanet.com/vortex-pro-series-30mm-riflescope-rings.html?_iv_tube-diameter=1-in&_iv_ring-height=medium-0-dot-95-in
Yes, it will.
At higher magnifications it is possible to have an issue with mirage from atmospheric conditions, however blurriness can be an issue of the diopter not being properly adjusted.
I purchased this scope within the past 30 days and the sunshade was included.
On the B22, we would recommend a set of the high-height Hunter Rings! PN# RING-H!
On this rig, a set of the Pro-Series 1" medium height rings atop a picatinny rail will offer minimum clearance!
This would be an outstanding option on your .17HMR. The parallax adjustment will range as low as 10y, and out to infinity, which is perfect for such a versatile rimfire cartridge!
The CF2-31033 does not require the use of a battery, as this optic has the non-illuminated Dead-Hold BDC reticle. The CF2-31029 is the V-Brite variant, which is illuminated, and the battery is housed in a small turret on the eyepiece!
The Vortex Crossfire II AO 6-18x44mm 1in Tube Second Focal Plane Rifle Scope does come with a screw in sunshade.
The Vortex Crossfire II AO 6-18x44mm 1in Tube Second Focal Plane Rifle Scope has a parallax adjustment from 10 yards to infinity. So it could be focused at 50 feet but the minimum magnification is 6x, so it may be hard to view an object at the close of range.