This handles up to .475 H&H recoil. It should handle both .50 Beowulf and .458 SOCOM (however by comparison, .50 BMG would be a bit much).
Yes, it can be used in the daytime. The unit under complete darkness will be limited as these digital night vision devices require light. With the illuminator included I'd probably put it around 150 yards + or -, but it will depend again on the conditions of the night and how much light the unit has to work with.
The S is technically better S model has a further effective range thanks to an improved IR illuminator over the non-S model.
The detection ranges are different because the two models come with different IR illuminators. The 850nm version (the S model) illuminates to a further distance than the 920nm version (non-S model). SightMark rates these up to .475 H&H.
This scope uses 30mm rings.
The S and Non-S versions have different IR illuminators. The Non S versions offer a 940nm IR that is invisible to the naked eye, some hunters like to make sure they are not detected when using the IR.