Comrades!

A few queries.
1 - The Fighters Guild is, essentially, a middle man between clients and potential employees, correct?
2 - Does the Fighters Guild handle contract killing?
3 - Is it independant?

(Off Topic) 4 - What is the extent of "criminals have no rights"? How does that work?

1) It's a regulated mercenary-for-hire organization created in the second era when guards and the army couldn't handle problems during the chaos after Reman's death
2) Only criminals, and even then I doubt they're allowed to kill on sight, unless the person is that notorious or fights back.
3) No, it's chartered and monitored by the Empire. Anything that's illegal or involves criminal activity is strictly forbidden. However, as seen in MW, there are loopholes.
4) eh?

Well answered in http://www.uesp.net/wiki/Oblivion:History_of_the_Fighters_Guild. The Guild arose in lawless times during the Second Era, to suppress criminals who were acting boldly and openly following the Potentate's suppression of local militias. Yes, it is the middleman for anybody requiring the services of a soldier of fortune, and for those pursuing that calling within the bounds of Imperial law and custom. Yes, it handles contract killing, so long as that killing is lawful (there are other enterprises who are not so picky). It is a creature of its Imperial charter, not independent.

The life of a criminal who does not surrender peacefully is forfeit.

I'm curious about the rules concerning a criminal's possessions, however.

Unless what they carried was stolen material, they mercs can keep it.

If the authorities declare someone to be an outlaw, then technically any citizen is allowed to kill them legally. I think that's the only case in which the Fighter's Guild can be hired as contract killers. Being named an outlaw doesn't mean someone will just go kill you though, so interested parties would have to hire someone to see it done.

And if they are carrying stolen material it is permanently locked away in a safe with few guards around it.