You can click on 'your settings', and on that page you can prevent
challenges if you have a specified number of games in progress. If
you change that to a small number, then nobody can challenge you
until you drop below that number of games in progress. You can set it
to 'zero' if you want. That should prevent all challenges. (If you go to
that page and change the settings, be sure and click the 'update'
button at the bottom of the page before exiting.
Any game when initially started will have a delete option available until
both players have completed a couple of moves. If you use that
option to delete a game, it will disappear and will not be reflected
anywhere as a statistic, and will have no impact on your rating.
It will be treated as if it just didn't happen.
Hope that helps!
Regards, Marc