The correct answers are Have you ever swum with sharks? and Have you ever slept in an igloo?

The present perfect requires a past participle.

"Flew" is the simple past of fly; the past participle is "flown" (Have you ever flown...?).

"Rode" is the simple past of ride; the past participle is "ridden" (Have you ever ridden...?).

"Swum" and "slept" are correct past participles!