If a person inside a house says they heard a noise but saw nothing, can a person be convicted of vandalism with no eye witness?

There are two types of evidence direct and circumstantial evidence. People can be convicted on circumstantial evidence alone. While having someone see the vandalism would strengthen the case, there may be other evidence that would prove you guilty beyond a reasonable doubt.

Absolutely, especially if you forget you have the right to remain silent and cop yourself out. Remember, no matter what you say it will be twisted around and used against you later.