These criminal record issues really depend on the jurisdiction in which the criminal record was incurred.
Many western common law criminal justice systems retain the rehabilitation principal of a 'spent record'. That is for specified classes of offenses the record will be deleted after a specific period of time. It really depends on the offense and what , if any, penalty was received for the conviction. It can vary from state/province to state/province. Even Singapore has this principal.
It really depends on the jurisdiction and the applicable law.
An arrest record from 28 years ago should not come up on a criminal record - especially as you state that the case was not prosecuted. Based on what you wrote, this should not be any impediment.
A DUI from 7 years ago is more likely, but you said it has been "dismissed" from your record.
What you need is a criminal check from your relevant law enforcement agency based on your current residential address (certified and translated for China context). Most operators usually accept a local/state criminal check. Some insist on National ones and depending on your country some criminal checks are only issued at a National level.
Obviously, residential addresses change though life for most pilots............