Are there alternatives to heart valve surgery?

Usually not - cause? Valve surgery is a long-term solution to a serious problem , usually no way to achieve similar effect/result without surgery. You can refuse consent, but you should be fully informed of the risks and expected outcomes before making any decision. There are different kinds of valve surgery depending on your condition. A complex issue you should discuss with your dr in detail.
Yes. It depends on which valve and the nature of the problem! there are percutaneous approaches but are very specific to certain problems and have limitations. You need to discuss your valve disease with your cardiologist and cardiac surgeon to explain all your treatment options surgical and per cutaneous.
Yes. There are options but depending on the situation they may not be very good. It depends on the valve involved, the type of pathology, how ill the patient is and the symptoms being experienced. Medical management is almost always done for a time (days to months) and can be appropriate for many patients. There are also less invasive approaches.