IIRC the dwarves have a place set apart for them in Mandos, so I guess they are reincarnated. I believe that is why there were so many Durin's. As for Hobbits, they are pretty much human so they probably have the same fate as Man.
Elves that travel over the Sea do not go to Mandos, they go to Tol Eressea or somewhere on the mainland where the other Elves already live. Now if they die, be it in Aman or Middle-Earth, their spirit will go to Mandos. Unless they refuse the summons, again I don't know if they could do that or not.
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