1. Chests/doors and many other things can be privatized. This is a plug in and if someone doesn't want you in their chest or in their door, they can make it so that only they can. That is probably why you can't go into some buildings or go into most chests.
2. TPrezzle is right, it can take 5 minutes or 2 days for an application to be accepted. Please be patient because there are MANY applications being sent in daily. When and if you are accepted, you will be notified and they will white list you and you can start your life in MineTown!