Welcome to the boards.
In answer to your questions.
1. The box sets do not come with the base inserts.
2. You can get whatever base inserts you like but the bayou inserts have recently been released and would fit best thematically.
3. Two box sets are enough for people to play (so long as you have the rulebook and 2 fate decks, or normal decks of cards). In saying that, some boxes are better than others in terms of the usefulness of miniatures in them and the points values. (For example, the ramos box can provide 28pts whereas I think the Gremlin box only provides 18 points.
4. I don't play gremlins so will leave this to someone else but I think so.
5. All outcasts with the mercenary trait can be used by other factions at the cost of +1 point over their base cost.
Hope this helps, enjoy your stay.