Answer: Sentence 1 and 2 are correct.
Wrung means to squeeze and twist (something) to force liquid from it.
Rung means a horizontal support on a ladder for a person's foot.
Sentence 1 is correct because you are forcing water out of the towel.
Sentence 2 is correct because she is performing the wringing action with her hands.
Sentence 3 is incorrect because rungs of ladders is written "rungs".
Sentence 4 is incorrect because the support of the chairs should be "rungs".
Sentence 5 is incorrect because the rungs of success is an analogy to a ladder, which has horizontal supports.
Hope this helps!