3 of 3 Corrected in accordance with DoubleAA's comment

Kiddush/chillul Hashem taken to mean showing the world that this is how Hashem's chosen people behaves:

No, by definition: The gentile cannot be representative of a group he does not belong to.

Kiddush/chillul Hashem taken to mean letting one self be killed rather than doing something for which one is required to let oneself be killed rather than doing:

Yes, by definition (at least theoretically): If that is the label of an act, and he did that act, then it has that label.* (However, as per Sanhedrin 74b, there may not be any actions requiring a gentile to sacrifice his life, rendering occurrence impossible.)

* My head spins from reading my own words!