Hexproof and "Cannot be countered"

Question

If I play a creature with "cannot be countered" and it has hexproof would either of them make it completely immune during the cast, because as I read something like Mindbreak trap can remove something with "cannot be countered" because it never resolved, but would there be a way around something like that. I thought hexproof but am not sure

Answer 1

No, to both ideas.

• The fact that a creature has hexproof has no bearing on the spell the creates the creature; see "Can I give a creature spell hexproof to prevent it from being countered?".
• A spell which "cannot be countered" stops only effects which say "counter target spell", for example Counterspell. It does not stop:
  • The spell being exiled, for example with Mindbreak Trap
  • The spell being returned to hand, for example with Unsubstantiate
  • The spell being put into its owner's library, for example with Aether Gust
  • The turn ending while the spell is still on the stack, for example with Discontinuity

Answer 2

All the other answers address parts of your question pretty well, but there's one more keyword that hasn't been brought up. If you're looking for a way that a spell can get around the non counter ways of removing it from the stack, the keyword you need is split second.

702.61. Split Second

702.61a Split second is a static ability that functions only while the spell with split second is on the stack. “Split second” means “As long as this spell is on the stack, players can’t cast other spells or activate abilities that aren’t mana abilities.”

702.61b Players may activate mana abilities and take special actions while a spell with split second is on the stack. Triggered abilities trigger and are put on the stack as normal while a spell with split second is on the stack.

702.61c Multiple instances of split second on the same spell are redundant.

If a spell (that doesn't target) both says it can't be countered and has split second, I don't believe there is anything in magic that would prevent it from resolving, all the methods of stopping a split second spell generally involve countering triggered abilities like the one on Kheru Spellsnatcher, which would be stopped by the "can't be countered" part of this theoretical card.

Answer 3

"Counter" applies to spells on the stack. "Hexproof" applies to permanents on the battlefield. "Counter" has no effect on permanents on the battlefield, and "Hexproof" doesn't apply to spells on the stack. Note that the card represents a spell while it's on the stack, and represents a permanent when it's on the battlefield, making Marc90's use of "card" less precise than "spell" or "permanent". When you cast a spell represented by a particular card, the default is that text on that card applies to the permanent that the spell will become. This default is overridden if the text specifically says it applies in a zone other than the battlefield, or it can't apply on the battlefield. For instance, since "counter" only makes sense while the spell is on the stack, it applies on the stack.

In addition, "Hexproof" only stops a permanent from being targeted. So if there were a card that said "Exile all spells on the stack", then even if Hexproof applied on the stack, it wouldn't protect from that card, since that doesn't use the word "target". Sundial of the Infinite ends the turns and removes everything from the stack, so it effectively counters everything on the stack, regardless of whether they "can't be countered", and without targeting anything.