Can you speed up carbonation times by setting your regulator to desired serving/maintenance levels and shaking/rolling the keg? Or is that a terribly bad idea (ala setting to 30 and rolling)?
It may have just been a fluke, in that case try again. If it happens again your plastic is most likely the cause and would need to be thrown out.
Is your nochill batch doing fine?
2) Just rehydrate dry yeast. The manufacturers don't suggest creating a starter.
3) Secondary fermentation doesn't do any fermentation, it should be called 'secondary clearing tank.' The purpose is to get your beer off the trub of the primary fermentation and help clear it. Some folks don't...
Go re-read the link I posted earlier: the spots at the top left and top right have a relatively long ways to go compared to the spots at the bottom left and bottom right. Your goal when designing this sucker should be to minimize the distance from any point to the exit.
You're unfortunately limiting yourself by only doing it locally. Do you think you could partner with a homebrew shop near you to increase your customer base?