I have my App on Google Play, Amazon Android Marketplace, and from my own site. Someone from Russia bought one from Google Play, and minutes later cancelled. Can I assume that Google Play has some mechanism that disables the App? If the customer bought it with the intent to defraud: order, download, install, run, cancel payment. What would be strategies for me to be able to do that via BT Self-Hosted Control Panel, etc.?

After you buy an app from google play you have a certain window of time until you can cancel your order and get your money back. Its annoying.

Can the customer still run the App?

No. They wouldn't get the app. However, I remember Google had a small blip with this a few years ago. For about two days, anyone who was refunded could still have the app. But two days later it was patched.

When a customer buys a download from me, from my site, then asks for refund, how to do disable it in turn?

You can't disable it from it being used if its from your site I guess. But perhaps you can prohibit refunds? You'll get very few that want to refund I suppose. I wouldn't worry about it. It is annoying but that is the game for some people.. But you'll have more customers that won't think of returning an app. Of course I don't know the price of your app but thats my opinion at least :)

in my opinion this is right.. as there are so many models and brands of smart devices with android , you can never be sure that your app will run as it should be in all of them.. recently i get a feedback from a user that uses my free version of my app asking if it will available (the pro version - paying ) for his device as one friend of him with the same device as he had , bought my pro version and never worked. So it is good for consumers can get their money back and avoid bad reports.