Back when Windows Store started, it only supported distribution of sandbox-based applications. I could only write something that displays in the Metro-style window and didn't have much integration with a desktop at all.
I need to sell an application that mainly resides in notification area and reminds user of particular events. As of March 2015, does Windows Store supports selling this kind of applications through it?
You can list your app in the store. The listing will link to your own commerce site to actually sell the app. Desktop apps cannot be hosted in or sold directly from the store.
See Windows Store onboarding for desktop apps