Can hair be taken from elsewhere than the hair on your head, or can you use someone else hair?

In theory you can harvest donor hair from any part of your own body.  You cannot harvest donor hair from another person because your body will reject it. 

While FUE donor sites from the body are well described and well published, scalp hair remains the best option for transplanting to the scalp.  When donor supply is exhausted, FUE from body sites can be used.  There are certainly advantages and disadvantages to body hair, but this certainly remains a viable option in hair restoration.

Transplant hair can be obtained from other areas of the body such as the beard,chest,arms and back but tend to not be the same quality as head hair.Hair transplanted from another individual would be treated as "foreign" by your body and attacked by your immune system.A genetically identical twin would be the only reasonable option in this situation.

Theoretically hair can be transplanted from any part of the body to another. The only issue is that the hair will retain it's initial texture, length, color, etc. so it may not look appropriate depending on where the hair is being transplanted from. This is why we prefer to take hair from the scalp for hair restoration before considering anywhere else.
You can't transplant hair from one person to another, however.

Hair
cannot be transplanted with success from one person to the next.   Transplanting your scalp hair to other areas
on your scalp usually gives the most natural appearance in terms of texture,
color and growth cycle.   However, when
the donor area becomes depleted, the beard, chest, back, and extremity hair may
be used.