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. 

Yes!   Hair can be transplanted from other parts of your body to your head, but you cannot transfer hair from another person.  Common areas for transplant to the scalp include beard hair (typically under the chin), chest hair, back hair, or arm and leg hair.  Over time local cellular factors on the scalp tend to help these body hairs take on a normal scalp hair morphology.  But, the best hair is good donor hair from the scalp.  Schedule a consult with an expert an find out what can be done.  Finally, if you are short on donor hair, you can consider cellular therapy.  Adipose derived stem cells and Platelet Rich Plasma are currently being studied for their potential to stimulate hair follicle development.

It is possible to take hair from other parts of the body, but it doesn't always match up so well so I prefer to not use it. It is however impossible to use somebody else's hair. The best hair to use is the hair that is found in the back and sides of the scalp of your own head. 

Hair transplants must by from your body, but it can be taken from other body parts like beard or body. Scalp hair is the best hair for a hair transplant