1) Does taking a hit while flying with cape count as "damage"?
The rules don't say anything about it. You don't lose the powerup, but it breaks the "no damage" clear condition, so imo it should count as damage.

2) It says no skipping of levels. So levels that require a damage boost are an instant loss?

@bundatbundat 1) Not allowed

2) Yeah, one little damage kill the run

Damageless category follow now the "Damageless Clear Condition" : Don't die. Don't take a damage by losing your power-up, hat, flying hit or "riding Yoshi, a shell or boot"