So once hired and through training, what happens if none of the bases are acceptable? Tough live with it
Is the company okay with floating? Can assignments be made to different locations during reserve? The company has Reserve pilots, but you have a "base"
How long time is given between passing the checkride until you must report to a new base once you accept a run? A few days depending on location
Is the list of current openings available for someone to post on here? No
Once you've taken a run, how soon can you bid for another one, and if you get it, can you pick up and leave your current run immediately? How flexible is it? You can bid as soon as you would like. However, if you are trained in something along with a baron and leave that run to another and "drop" an airplane you are going to sign a year contract. You have one "free" lateral too, so once you move your stuck in the base in most cases.
Edit: Oh, and are they having trouble filling classes and getting enough PICs to keep up with the attrition? Are they desperate and therefore easy to interview with, or will they look for any excuse to shrink the application pool? No we are not desperate to hire just anyone, but the hiring dept. are not a-holes either.