Although the details of the TD have not yet been decided, Bellumites will essentially be 'living' on it as they travel between fictional worlds. The time period will depend on the specific world, but they won't be 'living' there - their stay in the world is temporary until they move on to the next one. There will be periods of down time in between, however, so players and characters can have a break from the constant world-traveling.
As for time limits, it is reasonable to say that eventually a point may be reached where there is less variety in terms of fictional worlds to visit, but right now we feel confident that there is enough variety to keep plot going for quite some time - that isn't to say that we'll be sticking to the same repetitive things over and over, however. Variety and changing things up will keep the game interesting. :)
New characters will 'appear' aboard the TD, in the sense that it decides to snatch them up and take them along to join the rest of the pre-existing characters. In terms of open vs psl, we aren't going to openly advertise the game, and once things are starting off it will likely remain as a group psl for people to get comfortable and such.