Complicated question. The federal databases may not follow the same rules as state/local, so even an "expunged" state/local record might show up on a federal background check. Expunged or sealed means removed from routine access in THAT jurisdiction's records...a state CANNOT order the federal government to purge it's own records. Remember the feds use the data for national security/intelligence as well as law enforcement, so their standards are different...assume they will NEVER give up a piece of data once they acquire it.
There are three questions which you might asked...
1. Have you been convicted? You WILL get asked this since it is legal to ask in most states and it is also REQUIRED for the federal background check.
Convictions will almost certainly turn up on federal background checks, so there's no escaping it.
2. Have you been charged? This may not be a legal question in some states. This info might show up in federal, state, or local records, or it might not.
3. Have you been arrested? This is also not likely to be a legal question in most places. Airlines used to ask this, but I suspect that most no longer do. They might be able to ask if you have any UNRESOLVED arrests, where charges might still be pending since that could affect your ability to work as an airline pilot.
It may also be legal to ask about felonies, but not lesser crimes.
Bottom line, honesty is usually the best policy because it's too hard to know for certain if your name will pop up. Airlines don't usually run background checks until after you are in class...every airline pilot has seen someone removed from class after a week or two because their background check turned up something they "forget" to mention. Now they were officially fired from an airline for lying about their background...they will probably not be able to get another airline job. I would rather get turned away at the interview then fired after I had already quit my old job. That way when you do get a job, you don't have anything hanging over your head.
If you were young (under 25) when you got the DUI, that should not be an deal-breaker seven years later. As for the other charges, it all depends...
Peeing in public? No big deal, youthful silliness.
Possession with intent to sell, theft, violence? Bad news...