There is a one-year seat lock whenever you complete an initial type-rating in an aircraft. So, as a new hire, that basically means you aren't eligible to upgrade or add/switch types for one year.

Schedule is 12 days of availability followed by 3 hard days off. That changes to 10 on/5 off after 18 months on property (PICs only). I don't fly the King Air so I'm not in a position to comment on how many of the "on" days those guys typically fly.

It is possible to move bases or aircraft. It's based on operational need and seniority. There's also a seat lock - see my comment above.

And finally, no, commuting is not allowed. You have to live within about 45 minutes of a base. I know that's a major gripe for a lot of people considering EAS, but in my opinion it would be very difficult to maintain the "regional fractional" business model while having pilots commute. For me, the benefits of this job outweighed my hesitation to move (and after living in KC for almost a year now I have zero regrets), but obviously that's going to be a different decision for every person.