When I don't have possibility to eat something sweet, I start feeling very weak. This is diabetes or prediabetes?

To determine your diabetes status you should pass blood sugar test. The diagnosis will depend on the sugar level in blood.

After my recent liver transplant operation, I have been advised insulin doses (14 unit of Humalog at each meal and 22 Unit Lantus once a day). It seems sugar problem comes from medicine 'Wysolone' which, post-transplant, I am to take at 10 in morning everyday. Can I avoid taking insulin in morning - i.e. before I have taken Wysolone dose. Before breakfast my glucose reads about 115. If I do take NO insulin then after one and half hour of breakfast glucose reads 180 and then after further one and half hour it reads about 120. Is this normal or near normal and so can I avoid insulin around breakfast time at least without getting damage from high (is 180 high?) glucose.

High glucose right after breakfast is normal because you get some glucose from food. But you should not avoid this morning dose. We can suggest that your doctor has prescribed this therapy for limited time period, so it is better to wait and not risk your health. Good luck!