Not Advised. There have been some done in the past, but it is not advised. It could create a diabetic state in the donor. Since diabetes is not immediately life threatening, and alternative treatments are available, the risk/benefit to the donor seems too high.
Pancreas donor. Living donor pancreas transplantation is performed very infrequently and only at very select centers. Taking half of the pancreas is more involved for the donor than taking one of their two kidneys. For the recipient, it is a more challenging implantation. Perhaps if a patient with a lot of antibodies had a well matched donor and both were lean and healthy this would be a consideration.
Yes. Living donation is possible and there have been successes. Unfortunately, if things go wrong, you can start with one diabetic and end up with two. Therefore living donation has fallen out of favor at most transplant centers.
Yes. There are a few few places that do living pancreas donation. There have been less than 30 of them done in the us.