No. Double vision would not necessarily cause tire eyes. Most people only have double vision and don't have any other symptom. You may overuse your eyes such as playing too much computer games and cause tired eyes.
Probably yes. When you have double vision, your eyes will try to focus more hard to get a clear image and then get tired easily. But the most case is you will have double vision when your eyes are tired.
Maybe. If you have double vision, you can hardly focus on something clearly. Then you may try to overuse your eye to see them clearly, which make your eye muscles tightened. So you are easily to get tired if you have double vision.