Not sure how this works but ive had to start over a few missions because of having to go do something else.. this would be something id like to see improved. If its a design issue with the mission itself then there should be some good sticky post about how to lay out your episode for good continue/save points.
when i have played UGC missions and been disconnected or taken a break it will bring you back to the beginning of the mission but you can then manually map transfer all the way to the most recent map. its slightly annoying to have to skip threw several maps but you dont have to play the whole thing again.
im not 100% sure if there is any kind of time limit, or what would happen if an author republished it but i think you can pretty much skip to the last map you started.
if its all takes place on one map then no, it will just reset back to the beggining.
Normal, Cryptic created maps have the ability to store certain states of the mission so that returning to them later allows you to continue them from certain "save points". Foundry missions don't have that. I do not know why - it might be that storing the information is non-trivial. I remember that a dev said something that some missions store data "in" your character, so to speak, which allowed to keep some elements persistent in a map and re-use it later. That was not possible with the Foundry, but they were considering alternatives. Maybe that could also cover "mission states"...
It remembers which maps you have completed, so when you enter the system again it lets you jump through the maps you've already been on, until you get back to the beginning of the last map you were on. But if there was an objective like "kill 5 groups" on that last map and you had already killed 2 of them, you'll have to start that objective over again.