Here's the list, which I wrote before I posted the challenge.
1 Servalan (Blake's 7)
2 Emma Peel (The Avengers)
3 The Master (Doctor Who)
4 Shaun the Sheep (Wallace and Gromit)
5 Debra Morgan (Dexter)
6 H.G. Wells (the Warehouse 13 version, e.g. female, can time travel mentally, can't change the past)
7 Rupert Giles (Buffy)
8 Teal'c (Stargate)
9 Cameron (Terminator SCC)
10 H.G. Wells (the Lois and Clark version, e.g a time travelling meddler in search of Utopia)
11 DeliRIUm (Sandman)
12 Indiana Jones
14 Ducky Mallard (NCIS)
15 Tony Stark (Marvel)
Was I expecting someone who can fly to be chosen in a balloon challenge in the first response? no! But never mind...
major_clanger said "(2) Emma Peel, (5) Debra Morgan and (13) Supergirl are in the basket of a leaky balloon. Which one gets thrown overboard by the other two?"
Is anyone else boggled by the fact that all three have first names ending in A?
This one is only a problem if Supergirl is using her secret identity of schoolgirl Linda Lee, so let's assume that she is. Obviously she needs to trick the other two into throwing her overboard! The only way this can happen is if she pretends to panic and starts fighting the other two (taking care that they aren't thrown overboard), while secretly blowing the balloon into dense cloud. She then has to appear to fall overboard accidentally; she can then fly off and get Superman, Green Lantern, or some other flying hero who will pretend to rescue her and the balloon. Easy when you know how...
gonzo21 said "(15) Tony Stark goes on a mad killing rampage, which of the other 14 do they kill first and why?"
Obviously Supergirl if he knows who she is; she's the greatest threat so he needs to eliminate her before she can stop him. If she's in her secret identity it's a whole different ballgame, so the greatest threat might appear to be Teal'c or Indiana Jones. While he's taking care of the first couple of victims, Servalan slips him something lethal, bringing the problem to a quick close.
bugshaw said "(6) Ms. H.G. Wells and (8) Teal'c are tied up on a suspended platform above Doctor Evil's piranha pool. If one of the jumps, the other will be saved. How do they resolve the situation?"
Wells gets Teal'c to break her bonds, then uses the Cavorite concealed in her shoes to float them both to safety. No problemo...
maviscruet said "(1) Servalan, (3) The Master and (6) Ms. H.G. Wells are about to fight (5) Debra Morgan, (10) Mr. H.G. Wells and (13) Supergirl. Two versions of (8) Teal'c attempt to stop them. What the hell happens?"
Obviously someone has been messing around with the Quantum Mirror again, and at least one of the Teal'cs will die if the problem isn't resolved soon. The Master, being rather good at this sort of thing, quickly turns the Quantum Mirror into a Phantom Zone portal and traps Supergirl, but Mr. Wells escapes into the past and sets about turning his time machine into a Paradox Engine which will let him return to the present as hundreds of temporal duplicates, an all-conquering army. Ms. Wells uses her mental time machine to take over Mr. Wells' mind, learn the secrets of physical time travel, and trap Mr. Wells in a causal loop. Unfortunately this leaves her mind trapped in the loop too. This leaves two Teal'cs, The Master, Debra Morgan and Servalan. Debra suggests that she and Servalan should go to the bar and leave the boys to thrash it out. With them gone the two Teal'cs and the Master have a Staff versus staff versus Laser Screwdriver duel which leaves all three terminally zapped. Over drinks Debra and Servalan decide to take over the world. And there is much rejoicing...
curiouswombat said "(11) DeliRIUm wakes up and discovers (15) Tony Stark in their bed - how did that happen?"
DeliRIUm saw the suit and decided that it was really shiny, and gave it a cookie. After that Jervis was willing to do anything to get more cookies and followed her home, where the ARC reactor made it an excellent bed warmer. DeliRIUm didn't realise that there was a boring old human trapped inside the suit, until it was far too late for poor Tony. Fortunately DeliRIUm's doggy likes bones...
bugshaw said "(4) Shaun the Sheep is (12's) Indiana Jones' Secret Santa. What to they get, how does (12) Indiana Jones react, and how did they end up at the same Christmas party?"
There was very baaaaaad weather that Christmas, so Shaun knitted a nice woolly jumper for the Secret Santa. He was supposed to take it to Gromit's party, but due to a small misunderstanding with some mice and some wormholes ended up at Marshall College in the USA instead. Seeing the Secret Santa, Shaun dropped the present off then went looking for something to eat. A kind-looking man put his hat down just where Shaun could reach it - it was very tasty! When Indiana saw what had happened he called Shaun a baaaad sheep, but had a change of heart when he saw his lovely present. Now they are the best of friends, and often go adventuring together!
gonzo21 said "(14) Ducky Mallard breaks into (7s) Rupert Giles' email account, and is shocked to discover...."
...that Giles has been writing Twilight fanfic. Horrified, he borrows one of Abby's infallible murder methods, and uses it to rid the world of this terrible scourge.
bugshaw said "(3) The Master: "(9) Cameron, I love you, but we only have 14 hours to save the Earth!"
It was evident to Cameron that, although not human, the Master cared about humanity. Why else would he be working so hard to stop the Daleks from stealing the Earth's core? She only realised that the Master might have an ulterior motive when he tried to reprogram her to terminate UNIT and The Doctor.
That's All, Folks!