In general yes. The vast majority of transplanted kidneys are ABO blood type compatible. However, in certain circumstances ABO incompatible transplants can be done after extensive preparation of the recipient. This is usually reserved for live donor transplants where the extra treatments (plasmapheresis, intravenous globulins, etc) can be done electively before the transplant.
Yes. Blood type, or ABO matching, is important for all solid organ transplants.
Yes. Abo compatibility is a must when transplanting kidneys. O donors can go into anyone. Ab donors can accept anyone. A and b recipients can accept a and b respectively (as well as o). And o recipeints can only accept o donors. Under very stringent circumstances, you can occasional cross these ABO barriers but it involves greater risk of rejection and requires more intensive immunosuppression.