First off, welcome to the group and the game!!!
We're quite new to the game and just wanted to clarify game end - is it correct that you play until all of the cards in the draw pile have been used, then shuffle in the discarded cards, and that then triggers one last round?
Also, what is a 'round'? Is it all the way round with the first player marker (i.e. with every player starting first one more time) or is it just one more 'go' (i.e. first player marker passes to next player and you play that player's 'go'/round)?
It's the second of your options. A round begins when the First Player marker goes to the next player and ends when that player passes it along. Another way to look at it, each time you guys go through Phases 1 through 4 (Deal Cards through Feeding) is considered a Round.