No, I don't think people get married when they go to heaven but I can't think of any verses to back me up. Marriage just doesn't make since in heaven because you're a spiritual being who's purpose is to worship God. Heaven is filled with love so I'm sure you feel love for other people. But not necessarily romantically.
And you're right babies would go to heaven because they haven't sinned and they aren't old enough to comprehend accepting salvation. I would say the same goes for people who are severely mentally handicapped.