I have found for Safeguard, Bank first and then do the Side Missions. Mainly based on that extra time is best added after the bank.
For Mayhems, I do sides and destroy stuff first because you don't get extra time for destroying stuff.
I have never had any real issues though if I don't.
The jail never seems to come up as a waypoint for me on either, but I'm so used to it, and the Police Station is on the map.
And yes, you can reset time missions by talking to the contact, though I've normally just abandoned via the repeatable. Normally for the Invader badge, but I did it as well for the Safeguard version. (I have abandoned a Safeguard via the police contact, but not after entering. I think it should still work)
I'm not sure if that is something that was added since I don't think you used to be able to abandon timed.