Yes, if turn rolls, it is about the same as if you force End-Of-Turn by pressing ctrl-enter. Production is done, workers do what they are told, beakers are added to your technology bar, coins are added/sustranced from your stash, etc. If city finishes production, the next thing in the production queue is selected. If nothing is put in the production queue, then nothing is selected and you lose the hammers. Maybe with city governor turned ON, he can select something for you to put in production, have to test this. But it is highly undesirable situation if you lose turns. If you have RL situation which will mess with your playing turns, then you post here and ask for a pause. Or you ask some of your friends who play civ to play few turns for you with instructions from you or folowing his common sense.
And you can test this in SP, you just need to set up the game enabling the "minimize advisor screens" or something like this. In this case, you can hit EOT without selecting production or research or whatever.
About playing Bismark, I think there wont be much people wanting to play especially him, so I think it wont be a problem. But in principle, who plays what is selected either random, or by the so- called "Snake pick" - the list of players is randomized by the host or admin using random.org and then the first in this list chooses leader OR nation, then the second chooses until they go to the very last in the list and then they go upward. So the first to choose leader will be choosing nation last. This is with "unrestricted leaders" option enabled. But we can well play with restricted leaders as well. It just gives more options to choose from with unrestricted.
About the double- move, I am not 100% sure I understand your question. Yes, the game is with simultaneous turns, but because people are not all the time online, double- moves are forbidden. For example: your nation A want to declare war to a nation B. And you want to play before your opponent in the turn. Then you try to play before him in the turn before you actually declare him war. Then he plays after you. Turn rolls, new turn is up. You try to log in before him and then you can declare him a war. And from this turn on, until you sign a peace, you both must maintain this order - you play first in each new turn, then he plays after you. You are not allowed to log in after him in the turn, despite there can be a lot of time - you already played and hit EOT. And he is not allowed to join the game in the new turn before you finish your turn, because you are playing in the first half of the timer. Hope this makes clear. Ask any other things you might get as questions.