Can you transplant part of a pancreas?

The tail will do. The tail of the pancreas may be enough to cure diabetes in some patients but it is technically easier to transplant the entire organ. When it comes to islet cells (they make insulin), more is better so if you have a choice, take the whole organ.
Yes. Some centers will take the cells out of a pancreas transplant them into a patient. There are also a very limited number of programs working on living donor pancreas transplant. Neither of these however are very common.
Partial pancreas. The first pancreas transplant in 1966 was actually a partial pancreas (tail). Usually the entire pancreas is transplanted, although the tail has been transplanted in certain scenarios, for example in the situation of the infrequently performed living donor pancreas transplant or in the single report of an orthotopic pancreas transplant.