No, but you have to deal with assigned task in about 4 months. It's far much better (for me) than in early Arland and Ayesha.

Yes but not in real time

time flow only based on your actions.
gathering materials consume part of the day, and combat too.
traveling across macro areas consume days, traveling inside areas does not.
creating stuff with alchemy moves days forward too.

each ingame trimester you have a single assignment that you must complete, you can fail, i think, 3 times before game over.
you have several other tasks during this period, but they are for rank, bonuses, money etc. not mandatory.

I'll say that if you do your core assignment right away, you'll have at least 2 months worth of ingame time for whatever else you want to do.
it's very very lenient