Is it possible to do missions in nullsec?
sacrophyte
You bet. According to grismar.net, there are 954 agents in a system with a security <= 0. The Pirate agents are the more well-known ones, but even the Sisters of Eve have agents out in x-7.
Jonathan
NPC sov systems have agents for missions.
Good luck running missions out there if you dont belong to a corp that has presence out there. I'd have to probably say lowsec missioning is safer then nullsec missioning for the simple fact people cant bubble stations :P
gankman
Yes, but doing so is generally suicide unless you are friendly as others have said. My corp and alliance for example, in control of a decent section of 3 constellations in stain, prime NPC real estate. Even so you still have to watch for reds and random neuts running through. There are two ways to deal with this; either you mercilessly camp them out of existence so that it causes them to emo-rage and leave, or you move elsewhere/ add them to the often large blue-lists which prevail in such areas.
Always realize however, 0.0 changes. Join an alliance or corp that wants to go there if you cant get into one that is already there, and work to kick out a current resident or get into the blue-lists.
hoodoo
In NPC run nullsec yes.. like in the Outer Rings region where ORE is the npc corp.. but for the most part I don't believe so.