Don't know about refitting time, still didn't use it. But can say about rest things:
You spend 2 weeks for full repairs/refit between patrols.
And you don't really need to take missions at all. Because all this missions like "Patrol area till sinking any ship" or "Sink any warship in area" giving you only 1-2 skillpoints for crew
(and may be some renown, don't really know).
Global missions like "Eastern Coastal Waters" or "Western Approaches" you can do at any time. Just go to designated area and do what mission asking for.
When you ending patrol - you get skill point for crew too. I guess depending on your results in last patrol. I usually got ~15.
And one more thing - you can repair hull integrity only in dry dock - by ending patrol.
So, if you don't need skill points, new upgrades for your boat or even new boat - you can never end your patrol
