"There are so many" vs. "There is so many"

There are so many questions on this website.

There is so many questions on this website.

The former "sounds right," but the contracted form of the latter does as well:

There's so many questions on this website.

Which is correct?

It is There are so many. There ... are ... many.

People here are telling you that "there are" is right. In terms of any kind of Standard English, that is 100% true. When expletive-there + copula is used in the subject position, the copula verb is supposed to agree with the noun phrase to the right.

However, I suspect you are interested in also knowing if there is any significance to your intuition that "there's" sounds acceptable as well.

You are not the only one who finds that construction acceptable. The use of "there's" without regard to number agreement is increasingly common in casual US English. It is as if "there's" is becoming a separate lexical item of its own. Linguistically speaking, such a change would certainly be possible. Additional evidence for this hypothesis comes from what you mentioned in your question, that "there is" sounds bad, but "there's" sounds okay — this suggests some sort of disconnect between the two.