You get a new skin in HyperShot by opening a Case, skins aren't bought directly, they come from one of six Case tiers, Wooden through Mythical, with rarer skins having a lower drop chance.

No, a higher-tier Case doesn't guarantee a rare skin, it only improves your odds, the actual result from any Case is still random.

Not reliably, HyperShot doesn't publish an official drop-rate list, so treat any specific percentage you see elsewhere with caution.

Yes, you keep the Weapons, Skins, and Cases included with my purchase, exactly as shown in the listing.