Ya, it's normal. Some of my betta's "flarrers" are different colors then they. I have a black betta with red, blue with red, white with orange, yellow with see thru, etc. I'm pretty sure he is fine.
what kind of tank is he in?
it's not normal for them to mope around on the bottom.
mine did that for a week or so for no apparent reason
water change & salt and TLC, and he's all better now