Is there a way to stop my eyes from looking tired and puffy?

Yes. Cool compresses can help a lot. Make sure your eyelid skin is well moisturized to ensure it appears youthful. Artfully applied foundation and shadow can help a lot. If you have persitent puffiness around the eyes please check your thryoid status. Finally, if strongly desired, consider a cosmetic evaluation.
Depends on the cause. See an eye doctor to determine the cause then the best treatment can be outlined.