I love lucid dreaming. I love science. But this... this is very unlikely. What's far more likely is that planning a shared dream with someone causes you to have similar dreams. If you know each other really well, it would be fairly easy for your subconscious to replicate a person and their probable actions, especially if the two of you agree on something to do together while in the shared dream. Your subconscious can create detailed landscapes for science's sake! Accurately creating your best friends personality and predicting their actions in a scenario is cake. The fact that some of you claim the dreams are not identical, but share common signs isn't proof of shared dreaming, it's proof that you are influencing each others dreams by your interactions in the day time. If you spend the day with that person, the chances of your dreams containing similar images should be more likely than not. People appear in dreams all of the time, are you claiming that these people are all real people presently in their REM-cycles? That's a bit absurd, especially because people who are awake at the time I am asleep often appear in my dreams. What's even more absurd is to say that sometimes these people are real people and sometimes they are not...

It would be interesting to test, but from everything I've read in this post, all of your experiments are full of confounds and far from scientific.

The "Global Consciousness Project" sounds more like pseudoscience than anything. They claim they are attempting to test for a collective human conscience objectively, but they are correlating two things that have nothing to do with each other and then claiming causation. First off, claiming causation is nearly impossible, especially when studying something as intangible as this. You could just as easily say God gives structure to the random numbers when certain events happen. Also, they are using random number generators as a measurement when random number generators have never been scientifically established to measure anything. What does a collective human conscience even have to do with a random number generator? NOTHING! You could just as easily say there's a fluctuating magnetic field around the Earth that causes these generators to generate structured patterns. There are endless explanations and correlations you could make, but that doesn't make them true, nor related.

I have personally fancied collective consciousness theories and such, because I don't believe in God, so I enjoy thinking about other possibilities, but I am not about to claim these things are true based on faulty experiments.