No, the US is a republic if you want to be pedantic. We vote for representatives to make our decisions for us, we as citizens very rarely have direct say in stuff. Perhaps a hybrid between a republic and democracy would be best way of describing it.
Technically, no, he hasn't actually "won" yet. That won't happen until December 19, 2016, when the US Electoral College has their voting take place. While this will now be the 3rd election where the "winner" actually lost the popular vote, I don't know of any election where the electoral college votes ended up switching the outcome between the general election and the electoral college vote (I'm not saying it hasn't happened, just that if it has it hasn't been in recent years).