Baalei Aveirah in our midst – How to we deal with them?

Who’s a מומר?
Someone who flaunts his Aveiros publicly – is he a מומר?
Can a Baal Aveirah write an Ois in a Sefer Torah?
If the Sofer writes the outline is it kosher?
Can they get an Aliya?
Can they Daven for the Amud?
Are they Possul to be עדי קידושין?
Can they make ברכת הזימון?
Are we allowed to be Mechabed them or is it חנופה?
Should we be ostracizing them from our community?
Should we be Mekarev them?