Re: Should I wait or move on?
Wait for two weeks. Or for that matter, 4 weeks. No need to do background checks and investigation at this point. Once he is back, he brings his parents to your home and then gives a formal proposal, ONLY then you will need to do the investigation before your parents say say Yes or No to them.
For now, its too early. Carry on with your life, reply to him whenever he sends you an email. If and when we comes back and sends his parents to your home, and IF they like you and your family and gives a FORMAL proposal, then only you can take the matter seriously. Till then, relax.