Yes, contacts lenses can cause bags under the eyes. Because wearing contact lenses for a very long time will cause cutis laxa of eyes and that's one of reasons why bags under the eyes occur. So in order of avoiding eye bags, you shouldn't pull down your eyelids when you wear contacts. Instead, you should pull up your eyelids. Apply some firming eye cream to your eyes in day and some emollient cream to your eyes in light. Don't wear contact lenses for over 8 hours. You can do massage for your eyes which can help you circulate your blood in your eyes.
Of course not. Wearing contact lenses can not lead to bags under your eyes. Eye bags are caused by stress, lack of sleep for most people but I have never heard that it's caused by wearing contact lenses. So you should not worry about it. Well, you should know that there are some main factors which can cause the bags under your eyes, such as allergies, age, genetics, and the lack of sleep. So you should just check your own situation with them. Besides, stress is also an important factor. So you should have a good and relaxing rest, which is a good way to treat eye bags. Also, you can put cucumbers on your eyes and use Witch hazel.