By what means can a player faction become a DM faction? That is to say, is it even possible for a group started and operated by players to acquire NPCs or require applications for membership? How would one go about getting NPC guards or members for a faction? Are there any examples of this happening in EfU in the past, and how likely is it to happen?

Having NPCs around doesn't really make it a DM faction per se, but usually getting NPCs to join a player faction is a result of the faction's IC actions, longevity, and quality contribution to the awesome.

How would one go about getting NPC guards or members for a faction? Are there any examples of this happening in EfU in the past, and how likely is it to happen?

A good question, and there are multiple examples actually. Likely the best known to the player base is the House Toboerski (sp?), in which Oro did an ass load of RP over a period of months to build up his own PC based House Guard, drove each of them to pursue House goals, and then IG made the deals he needed to to gain additional support ending up in quite an NPC presence.

Anyone who devotes the time, investment of RP, etc into a concept has the opportunity to recieve extra support in this manner. It does need to be earned, as long standing retainers are a very powerful thing to have.