Hi,
If I voluntarily change employers, can my old employer make me pay back any USCIS fees that they spent on my petiton? Also can they make me pay back the attorney fees that they spent when they filed for my petition?

Thanks

Ideally it's your company who is responsible for USCIS fees + Lawyer fees and not you.

But if you had signed any bond (like you will work for at least 1 year with them) or employment contract (like you need to give x-days notice) which you have broken, then they can send you a legal notice for the same claiming for damages. Usually the employers use it to scare the H1 guys but there have been times when they DO really come after them.

Here's a very good US Dept of Labor explanation for this topic that I found a few days back:
Fact Sheet #62H: What are the rules concerning deductions from an H-1B worker’s pay?