You can close the window and vote again. It does appear to increment the vote.
Nope. The return message changes from "Thank you for voting!" to "Thank you, we have already counted your vote."
It happens even if you vote from a different computer behind the same NAT router. So, they are going by IP address, not playing the usual cookie games.
I managed to triple-vote by routing my connection through two separate VPNs, one in NH and one in TX. So, they saw three votes, from MA, NH, and TX. I brought up the page in an incognito window each time and got the "Thank you for voting" response.