Firstly, I always thought time in a dream is the same as outside if not slower.
-Can time actually occur faster in dreams, or whatever speed it would be called?
-Is it possible to use sheer willpower to enable yourself to continue dreaming?
(And if so, would that cause a coma like state?)
-If you have psychic powers, I don't think I do, could you do networked dreaming?
(Shared dreaming in which both people are in the dream conscously?)
-Is it possible that, while lucid, if you chose to do something like working out, or mentally choosing to increase production of testosterone, that if you (had already in real life) work out it could potentially effect you in reality?
-While lucid, if you remember where you fell asleep, is it possible to purposely bypass the sleep paralysis to try to sleepwalk( *and grab a sandwich from the fridge)?
(Well maybe not a sandwich, but like an extra pillow or something.)
-Is it feasible to have a goal of lucidly dreaming every night?
-The manipulation of the dream world is possible such that one could transform, generate things, do lotsa cool things, and maybe even go to the theater?
(Has anyone tried watching a movie or reading a specific book in a lucid dream on purpose successfully? Oh and can you make paradoxical structures/buildings?)
-Is it possible to remain conscious when transitioning from REM to NREM back to REM??
-Is it actually possible to gain a skill, practice it anyway, while dreaming?
-Is it possible to use your dream to access things in your mind that you otherwise can not remember?
-Is it possible to project real things form memory, like a book or string of numbers?
-If you could bypass the sleep paralysis mechanism, could you dial a phone?
More specifically, would you be able to incorporate sensory stimuli into your dream?
(Such that if you were listening to a tutorial on audio perhaps you could learn it while dreaming? Maybe listen to a guide on painting and paint the sky in the dream?)
Can time actually occur faster in dreams, or whatever speed it would be called?
Yes your mind can perceive time in dreams differently than real life!!!
Is it possible to use sheer willpower to enable yourself to continue dreaming?
(And if so, would that cause a coma like state?)

Yes actually but you wouldnt get in a coma state I don't think. Remember though the dream always has to end.
If you have psychic powers, I don't think I do, could you do networked dreaming?
(Shared dreaming in which both people are in the dream conscously?)

That's up for debate. A lot of people have claimed to have shared dream (I believe it real) but it's not scientifically proven.
Is it possible that, while lucid, if you chose to do something like working out, or mentally choosing to increase production of testosterone, that if you (had already in real life) work out it could potentially effect you in reality?
Again up for debate.
While lucid, if you remember where you fell asleep, is it possible to purposely bypass the sleep paralysis to try to sleepwalk( *and grab a sandwich from the fridge)?
(Well maybe not a sandwich, but like an extra pillow or something.)

I don't believe so.
Is it feasible to have a goal of lucidly dreaming every night?
Of course but it might take some time!
The manipulation of the dream world is possible such that one could transform, generate things, do lotsa cool things, and maybe even go to the theater?
(Has anyone tried watching a movie or reading a specific book in a lucid dream on purpose successfully? Oh and can you make paradoxical structures/buildings?)

Yes the whole world in your dream is yours. Build or destroy as much as you choose.
Is it possible to remain conscious when transitioning from REM to NREM back to REM??
Not sure..sorry!
Is it actually possible to gain a skill, practice it anyway, while dreaming?
Up to debate.
Is it possible to use your dream to access things in your mind that you otherwise can not remember?
sometimes.
Is it possible to project real things form memory, like a book or string of numbers?
Yes.
More specifically, would you be able to incorporate sensory stimuli into your dream?
You can include all senses in your dreams even though what your feeling or smelling or tasting isnt really there.