I haven't found the answer to this question in the help text yet...
The change to the next quarter is every night, I guess around 4 am. So there is only one quarter each day in real time.
Once per day. Around 3 am CET the calculations following to your decisions are applied to your state.
Well i started playing yesterday, but i haven't recieved a new quarter today.
Oh, the new quarter is winter, yesterday was autumn. In winter noone does receive new tasks, but you may change your budget und "Details". And RTFM

And I can only handle one task (and reform) at a time, right?
And I can only handle one task (and reform) at a time, right?
Only some tasks (1 to 3) or reform
and in winter - no tasks, but reform or household.
Only some tasks (1 to 3)
or reform

and in winter - no tasks, but reform or household.
Thanks! 
@Game-Designer: It really would make sense to put such an important information in the manual.
Each day of real time is one quarter year in the game.
It's there... 