How can one be certain that the suitor is free of sexually transmitted diseases, given his repentance from his past, and how can one be reassured about him Islamically?

The basic principle is that a man is free from diseases, so it is preferable not to demand a medical examination from him, for infection does not transmit except by the permission of Allah, so rely upon Him. However, if you insist on an examination due to your suspicion of his infection, then that is your right. It would be even better if you could achieve this through an artifice, via some of your relatives.