Yes, it is possible for you to get pink eyes from diabetes because of the weak immune system. However your pink eyes could also be caused by the contagious character and other infection at the eyes. You need to have the good rest for the pink eyes and use some eyes drops with anti-inflammation to cure it.
In my opinion, it cannot lead to pink eye. And it is very normal to have this kind of disease. Of course, when it occurs, some symptoms can occur. For example, people with this disease will have retinopathy, cataracts, and glaucoma. Also, it can lead to floaters in your eyes and that will make you feel annoying. Besides, according to some experts, it can lead to weaker blood vessels and have a high potential for problems later. But it cannot lead to pink eyes which are often caused by eye irritation.