They're not exactly a crime-fighting organization since they're up to quite a bit of it themselves, so sure. I think redirection would fall under the regulation they're attempting to sell themselves with.
I haven't read Discworld, so I'm not sure. If an organized crime group were trying to do their best to make themselves feel valuable and worth tolerating though, they'd likely be interested in making sure the crime that does go on is "sanctioned" and so do their own part to deal with troublesome independents as part of proving their worth as a society. Clarifying note: This shady society is not an assassin group. If they're interested in being tolerated by society and the governments they work beneath/within, it's in this society's interest to draw certain lines and make it clear and apparent that they're more valuable than detrimental to have around. Specializing in assassinations and being frequently responsible for the murders of citizens would make that a pretty hard sell, so they tend to stay away from that kind of thing and prefer to instead put on pressure in other ways when necessary. Not that an occasional convenient death of a particularly problematic individual due to mysterious circumstances would never occur, but it's something this society certainly wants to avoid if at all possible.2. If you've read discworld, is the shady society's crime strucsimilar to the thieves and assassin's guild? i.e. people who are not affiliated with the aforementioned guilds are delt with?
I think a case could be made that it could be in the Dominion's best interest to work with this organization in order to regulate crime, at least in the short term while the Dominion is still in its infancy (which it currently is). The Dominion would of course wish to be the sole entity in control eventually, but at the moment it'd likely be much more practical for them to tolerate and perhaps even occasionally quietly work with this group who is regulating crime and maintaining a sense of order in their own way. If some of the rumors are to believed, they have remarkably similar aims in cultivating a prosperous and orderly society - just different ideas of how and why to go about that.3. will wanting to be a part of this society be going against the dominion's code of peace, order and prosperity by being a part of a group that is linked with crime?
P.S. If question 3 is essentially asking "would a Dominion character be able to join this Society without worrying about being kicked out of the Dominion for mere association", the answer is "yes." They'd have to take care to not do something foolish or offend the wrong person, but it's by no means impossible to walk that line. I could see some (certainly not all, but some) true blue believers in the Dominion vision of peace, order, and prosperity thinking that this society is of legitimate value and is a useful means of achieving said vision.