Well, i’ve had 2 dreams which weren’t lucid, but my body was transformed(i didn’t ask the dream for that while i was asleep,but i did the day before) into a pikachu both times. Neither times answered my other question, but one felt more real than the other. Which was the time I didn’t ask at all, and happened in the middle of the dream, is this common? Both times only felt like my height was affected, but the second time I might’ve went on all 4’s a bit…
Yep, that’s normal. Doesn’t happen to me personally, but other people transform into animals in dreams (or fictional animals) fairly often.
Oh yes it can definitely happen and it is normal! I myself have yet to change into an animal but once I did change into a woman. It was uhmmm, very interesting. 
I change into a bear a lot in my dreams. And a male, every now and then. Perfectly normal, and can be pretty interesting once you wake up. 