Once you finish a quest, does it disappear forever and you can't complete it again, or does it just cycle through them randomly, even if you've finished them already?

They cycle round and round in a randomish fashion. Although I think you get lots of easer ones when you first join HEE.

I just completed the 'breed a premium brindle foal'. That is a tricky one, took around 5 weeks as brindles happen only rarely.

Good luck.

You can get the same quest many times, they just cycle randomly :)

Thanks guys!