In the movie The Fly, a human and a fly are fused together when they are both in a teleport pod during it's activation. Would the same thing happen in Star Trek if two lifeforms were to be transported together?
Not normally but depending on the writer, it could be possible. The thing to remember is that it is a fictional piece of technology with loosely defined rules for how it works, but it also has tendency to break down when a writer wants something terrible to happen to people to create a story element. Like
- breakdown and horribly mutate and kill Commander Sonak and someone in Star Trek: The Motion Picture
- breakdown and merge Tuvok and Neelix, on Voyager's 'Tuvix' (because of some plant though)
- breakdown and make two Will Rikers, TNG 'Second Chances'
- breakdown and split Kirk into good and evil versions, TOS 'The Enemy Within'
- breakdown and send Kirk and people to the mirror universe and vice versa, TOS 'Mirror Mirror'
- still being an experimental phase, they beam Novakovich up off the surface of the planet in Enterprise's 'Strange New World' while in the middle of a storm, and when he materialises leaves are stuck in his skin!
This last item I find to be the most compelling that something like what you are suggesting could happen, without any interference and simply having the transporter malfunction, although that was at an early stage of it's development (Emory Erickson, inventor of the transporter probably has hundreds of horror stories about it's development, like people beaming into solid walls, half-cat/half-dog test subjects, lawsuits because of de-nudification etc etc). But, more closely, simply adding that plant into the mix in 'Tuvix' had a much more similar effect to what you are describing. So find that plant, David Cronenberg and a fly, well....
Something to remember: TOS had transporter malfunctions as a common occurrence for a plot device. Similarly, TNG had holodeck malfunctions, but by then the transporter was generally fairly well established tech. There were also plenty of examples in TNG where two people were touching or even gripping one another and teleported in situ, able to separate afterward with no problem.
I would, however, point out that there is a distinct difference between physically fusing two bodies together and what happened in The Fly. Paraphrasing from The Fly "Something went wrong. The computer was designed to work with only one body, not two, so it did the best it could." In The Fly, the main character's body (including genes) become a fusion of the two bodies, but simply attached to each other.
Tangentially, The Fly II (which I coincidentally watched last night) doesn't offer the slightest explanation for any of this- why it used to work, why it stopped working, how the problem was fixed (I'm sorry but "The scientists couldn't do it because they couldn't see the beauty of it" is not an explanation). There, though, it was dealing purely with genetic expression of (sort-of) junk DNA. Incidentally, why a live body was required I don't know- I would argue that he killed more than enough people in the final scene for it to be easy to find a body to take the morphs.
So, I've meandered this a little bit, but the explanation from the movies seems to be that the computer combines the genetic code of the two creatures to make a fusion creature, rather than physically attaching them together.
Yes. It has happened before. The transporter is specifically designed to avoid this, however, so it is a freak occurrence.
I would expect that two people would simply fuse into each other and the resulting mass would die almost instantly due to blood vessels and veins being blocked off by the matter of the other person, down to the very cells unable to function again because of being blocked off inside.
Also, how come the writers didn't simply have the transporter phase someone whole body out of normal space and place them elsewhere via a (subspace?) tractorbeam vs. trying to take someone apart at the quantum level and reassembling him/her thousands of miles away? The first is far more realistic. The tractor beam can even contain an air pocket so aphyxiation would not be a problem