FYI: The FCRA (fair Credit Reporting Act) says that no backround check company can notify an employer of pending criminal charges for a prospective employee. So if you have no convictions, your pending charges will not show up UNLESS your employer does a local public record search which is very rare. All arrests are a matter of public record and can be accessed by anyone. It's very rare that employers do this though.
Now as far as what they can ask you, basically they can ONLY ask you about convictions. Here is a really good link regarding the laws in the state of NY.