My group is on a run and we get into a shootout. My character knows that the enemy has vital information that my character needs, so he tells everyone to leave the leader of the goons alive.

After the shootout my character goes to the surviving enemy and begins interrogating him to try and get the information out of him. Suddenly another player decides that his character tries to shoot the man dead during the interrogation.

Now, would his character get to shoot the enemy before I get to do anything? Or should we roll initiative to find out if the other player's character can shoot the man before my character can do anything about it? How about a surprise test?

Well that would be pretty surprising, especially as your character is approaching the target while one of your party is probably drawing behind you to shoot him.

I would say go with the surprise roll (pg 65, SR4Anni) then the init roll.

Of course if the other guy does win the surprise and shoots the baddie your character now has a dilemma, namely WHY your teammate thought it vital to shoot the guy that you specifically wanted left alive.

Did the rest know he had information you wanted badly? Maybe your team mate is working for the other team and didn't want to be outed so had to take action.

Either way his actions should be the source of much amusement as you get to practice your interrogation on HIM.

Yeah, that's how I would do it too.

Problem is, my DM ruled that he gets to try and shoot him without me getting to try and stop him. I plead to get at least a surprise test with a major penalty to no avail. He, of course, used Edge and everything and killed the guy in one shot.

They didn't know that I needed information from them, I just asked them not to kill everyone. The goons had dressed their hostages the same way as themselves but with red bands around their hands, so the others assumed I knew the leader was someone real important.

The another player is playing a sociopathic and reckless Black Magician, so he does everything "for the lolz". Irritating to play with, but the others have played with him for a long time and have no problem with him for some reason...

Well the GM does have the right to make that call. The surprise test is there more to protect the PC from being ninja'd too easily, but NPC usually do not get that luxury.
Also the GM may know this character and considered what would happen if you had actually won the surprise roll (unlikely given the factors that probably would have tipped the odds in the mages favour), would you have stepped in front to block the shot or even shot the mage? Would the mage have taken the shot anyway?
The GM may simply have wanted to avoid direct player to player conflict, or maybe he didn't want to fork over the data the leader would have had just yet so bought himself some time by letting the mad dog have a chew.

Ah.. this is what we call mission creep.

Your objective and the team objective were not necessarily the same and you did not tell the team your full objective, hence you feel let down by the team for their actions, but you also have to recognize that if you had told them in advance then they would have been able to try and fulfil YOUR objective.

Was the Black Mage going a bit overboard? Probably, but would he still have shot him dead if you had told them you needed information out of the leader?
If not, then that SNAFU falls on you.
If yes, arrange for a convenient but entirely fatal 'accident' for him because sooner or later he will probably try to get his lolz out of you or consider a different group if they are not your style of play.

Next time, offer to let the Black mage 'help' interrogate, nothing like a round of good cop, bad mage to get info out of someone, especially if the guy IS a sociopath and projects it well.
This will at least encourage him to keep a few alive, if only to get interrogated.
WARNING: If you are not ready to witness/stomach a Black Mage doing a proper interrogation, you may want to skip this option.

What? You seem to think that a Black Mage is potentially more creepy than any other mage.
I have a Black Magician on my payroll that would like to Chat with you on this matter.
Please report to "Conference" room 7.

*dispels the Bone Etching Spell and sets his apprentice to tidying up and prepping the subject for the next round...*
Now I never said that at all. I was merely pointing out that the aforementioned sociopathic Black Mage (the one who shot the captured gang leader prior to letting the OP get a chance to interrogate him) may well enjoy the session, but may be unsettling for the OP to observe.
Great, another meeting with Ms. Dommie from Inhumane Resources for Sensitivity Realignment.

But then again, maybe some time on the Rack will get this old crick in the back out.

With a S&M Dance
Sendaz

If this is the only character you've seen him play, perhaps part of it is that this isn't the usual sort of character he plays.

Well, I've seen him play a sociopathic (his words) shugenja who hasn't been taught anything about honor in L5R and a suicidal pilot in Rogue Trader who always had to do the most insane stunt he could think of, risking our spaceship and all it's crew. When we played D&D he picked druid and then complained that druids aren't good for anything, even though he soloed at least two encounters made for a party of 5 with some rulebending.

You decide

But basically, if there was another group in my city I would join it in a heartbeat. So far I've only found groups that never play or people looking for groups. They join our group for a couple of sessions and most leave after that.