Immigration officers check your travel documents, luggage and ask you questions about you and your reason for visiting. If you are "flagged on their database" then they shall make further enquiries. There is no form to request disclosure.
You can engage a Thai lawyer to make enquiries with the Thai Immigration for any Prohibitions or Restrictions.
In practice, 10 years is a long-time! Unless the criminal offence was serious and could pose a threat to the good morals and order of Thai society
Depends on the nature/type of the criminal offence and whether either the [US] authorities have communicated it to the Thai authorities or the [US] Embassy may notify them.
As it was 10 years ago, it is likely that neither the Thai authorities nor the [US] authorities shall consider you a danger to the Kingdom.