Legal Question in Criminal Law in Kentucky

That depends on what the question actually asks. Depending on how the question is worded, it may not be asking you to divulge your now-dismissed misdemeanors. Answer truthfully, but don't provide more information than they're actually asking you for.

If the question is "Have you ever been convicted of a felony?" you can honestly answer the question as "no." If the question is "Have you ever been charged with a crime?" the answer is "yes." However, if it's "Have you ever pled guilty to a crime?" that one's trickier, because even though the charge was diverted and ultimately dismissed, it still required a guilty plea to enter the diversion program. The Feds might consider that answer to be "yes."

Even when charges have been expunged, in the age of internet, it never really goes away. Regardless, screwing up your bank account, probably from closing your account before all your checks cleared, probably won't matter to the FAA. Concealing it would though. You should answer the question truthfully and accurately. It is more important to be candid than it is to have a clean record and failure to answer truthfully could have criminal consequences as well.