First, yes, as Stephen mentioned, 1 coat of stain is always best. If you do 2, the poly doesn't stick well.
Second, my guys usually leave the stain on for 2-5 minutes. It can vary a bit by the stain and generally less time for the darker stains.
Third, yes, the edges should blend. While I haven't seen your pictures, based on your description, it doesn't sound like they sanded/used the edger properly on those areas/didn't transition well.
We prefer to use duraseal (made by Minwax), but we often use Minwax as well - depends on the customer's color preference.
Debbie Gartner aka "The Flooring girl."
http://TheFlooringGirl.com