So I've noticed you're given 3 weeks between each story quest. In the 3 weeks there's always been 2 side quests so far I've seen and a spare week to visit the shops.

My question is if you don't use up the spare weeks between the story quests, do they accumulate after each story quest. I.e if you have 1 spare week left but you did the story quest, does that mean you will get 4 spare weeks after completing it to the next story quest?

Yeah, in the campaigns at least if you do the campaigns, if you do a plot quest right away you'll have 7 weeks the next time etc. After a certain point though you want to stop putting off side quests because you need the gear.