1. The Armature modifier is essentially how you connect a mesh to an armature object. It’s not unlike the “skin” modifier in 3D Studio Max, if you’re familiar with that.
You leave the modifier there. Exporting out of Blender via FBX (for example) will do what it needs to with the armature modifier. But that’s another topic entirely.
2-3. We have several rigging courses: https://cgcookie.com/courses/?fwp_division=blender&fwp_education_subject=rigging
4. Those are some big questions. Kinda the point of Rigify is to *not* have to touch anything within the rig. If you want from-scratch rigging, watch the rigging chapter of the Piero course: https://cgcookie.com/course/short-film-character-production/
Again, some more big, technical questions. Are you brand new to rigging?