More of a pre-lucid dream question... can you dictate the content/topic of your dreams? That would be some powerful stuff - virtual reality of another kind.
I've had quasi-lucid dreams. I have free will in them (and certain "learned processes" such as flying), but I am not aware that it is a dream until I wake up. So far as those go, I can "physically" escape settings that I don't like but I can't decide what settings I end up in. I'm generally stuck with the people the dream starts with and they always have their own free will.
Yes. Once you're fully lucid you can do anything. I've flown across the US, into space, banged movie stars in the white house, drove Ferraris off cliffs, etc... Since your thought process is a bit disorganized the hardest part is deciding what to do on the spot, knowing you've only got a few minutes to an or so hour max
I don't have that much power. For example, I can indeed fly, or jump as high as I want, but I have problems creating objects or people out of thin air. It seems easier for me to imagine that the object is behind me, and then turning around, then it mostly works (not always). And people in my lucid dreams sometimes have their own will, so I can try to bang anywhere (knowing that I won't hurt real people and there will be no police) but I get rejected sometimes :)
I suppose it's all a matter of practice or of becoming more lucid, though.
Sometimes things don't end up like I wanted either, but I've gotten pretty good at "ejecting" those situations rapidly, a few seconds, in favor of what I'm looking for. Not absolute God Mode, more like browsing an unlimited movie collection for what you want