Can I take birth control pills but not to control birth but for my hormonal imbalances? Like to have better skin etc. Thanks

Yes. Talk to your doctor about the pros and cons (nothing is entirely without risks or side effects), and they can prescribe for you if you decide this is right for you. If hormones aren't the right answer, there are other options for treating acne, unstable mood, cramps and other symptoms often relieved by birth control.
Yes. But it may take fine tuning. The original research for the pills was based on such issues and control of abnormal menses. The birth control was a side effect that became the main selling point.