If two players have played a series of games, is there a way to play through the entire series automatically (in real time), as opposed to playing through each game one by one?
I am not sure I understood the question. Go to your profile > Either click on blitz, classical, bullet > you can search the opponent's nickname on the top of the page, near "Opponent name". Select "human" and then type the nickname.
#2 shows you how to find this series of games, but I believe that you have to watch them individually. You can download these games and there are database programs that will automate the games, but I still haven't found one that will advance to the next game.