If my opponent casts Ultimate Price on my Phantasmal Bear, can I save it by casting Snap or Curfew?
You can save your Phantasmal Bear with Curfew, but not with Snap.

The "illusion ability" is a triggered ability, and once it triggers it goes on the stack on top of whatever spell or ability triggered it. So, after your opponent casts the Ultimate Price, the triggered ability goes on the stack and then you have the opportunity to respond. If you respond by casting Curfew, you can choose to put the Phantasmal Bear into your hand, which will save it from both its own ability and the removal spell. If you instead respond with Snap, Snap itself targets the creature, so the illusion ability will trigger again and go onto the stack on top of Snap, and you will have to sacrifice the creature before Snap resolves.