I juice carrot juice for my DH a lot. I don't peel the carrots but I do cut off the stem end. I think it is best juiced "as needed" & not stored as in gallons. I think it looses it's flavor if not used immediately.
I would not juice the orange/lemon peels along with the fruit. I think it would tend to give it a more bitter taste. I would use the concept of....if you wouldn't eat it outright, don't juice it. I wouldn't eat an orange peel so therefore, I would not juice it with the orange.
I've always wondered what to do with the "plup" of the carrots that I juice. Well, I've not come up with a good answer so I just throw it out for our wild country critters like the opposums, rabbits & such.
I have a pretty strong juicer so I would think it would handle nuts but I've never tried them in with the other things I've juiced.
Once we were drinking so much carrot juice that we started looking a bit "orange". So, we slowed down of the carrot juice. Now granted we were drinking LOTS of it when we first got our juicer years ago...and I do mean LOTS.
Hope this bit of information helps in some way.