The Baby Jogger City Versa does everything on your list. Not many prams that face both ways fold with the seat on both positions. They are a bit hard to find at the moment as the 2014 models are due soon and they are clearing 2013 stock - but you might get a bargain this way. I love the quality of Baby Jogger. I have a City Mini, which does come in 4 wheels and rear faces with the capsule or by adding a bassinet.