Yes, of course. That's the cost of same-sex marriage in such a game, unless you use the House Seniority mechanic you will eventually have a game over. That doesn't make this anymore difficult than switching a false to a true in an optional fun feature, it'll just be very difficult to play the game (but not impossible!)

Elective succession and tanistry were rather common historically and an option in the game, so having kids shouldn't be significant. The key is the heir has to be in your dynasty, not that it be the fruit of your loins.

Well, one can have kids from other partners, not only within marriage.