If they send you an application, they plan to hire you! No games are played here unlike, UAL. The process is quick, my suggestion is to take the first class date or airplane you can, unless you want to wait while.
In terms of flying from your home or your domicile. Not sure about that one. Its my feeling they will airline you from your home. After training is completed, you will then be required to be within 90 nm of your domicile.