1) When a civil war marker gets placed on a power that had a disaster marker on it, does the disaster marker get lifted? A strict reading of the rules says a disaster marker only gets lifted after an income action takes place and you collect money from the power's controlled regions.
I assume therefore you can have both disaster and civil war markers on the same card. By this logic the same can be said for excommunication markers and civil war markers. One does not replace the other, but adds to it.
Indeed, if the rules do not tell you to remove a marker, it is not removed. You can have a Disaster, Civil War, and be Excommunicated all at once!
2) In one game, one player conquered Hungary. As it is a single province power, he also took the card to control it. Can he for a second attack launch an attack from Hungary immediately?
Are you using the "living rules" from 2004? I ask, because there is a clarification in the Power Control section (4.3) that addresses this very question. Yes, you can gain control of a Power and then use it for your second attack.