The big rule to remember is that grammar is intended to make communication clear and free of misunderstanding. "Yes it's" isn't even close to being clear.
When you use a pronoun (in this case, the 's) the listener/reader needs to be clear about what it refers to.
If you were to say to me - "Yes, it's" instead of "yes, it is" I would be waiting for you to finish your sentence. Yes, it's ....doesn't mean the same to me as Yes it is.
Is this the correct answer to Problem #3?
Yes, it's.
I would wait and then go, yes, it's what? I would want to be as clear as possible, so I would also err on the side of being understood first,
As Didge indicated, if those are the only words in either sentence, what you are saying is not clear.
The contraction it's requires a predicate noun, adjective, or adverb (or equivalent phrase) to convey the meaning of the sentence.
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