Will eye exercises or an eye patch help ptosis? Will Botox or surgery help with asymmetry?

You need a highly experienced ptosis surgeon to address your issues.  This will be a fellowship trained oculofacial surgeon. Ideally you will find a surgeon who both does ptosis surgery and aesthetic surgery.  There are two basic forms of ptosis surgery.  You have a disinserted anterior levator tendon.  This must be repaired with an anterior levator resection ptosis repair.  Posterior ptosis surgery (mullerectomy) will not be satisfactory.  You also need the crease reconstructed.  The eyebrows will relax to a more normal position when this is done.  The American Society for Ophthalmic Plastic and Reconstructive Surgery maintains a geographic directory on its website that can help you find a highly qualified surgeon close to home.

Although you have mild upper eyelid ptosis, the appearance is worse since there is also hollowness in your upper eyelids area. See an oculoplastic specialist for evaluation. See following link and video too.

Hello and thank you for your question.  The best advice you can
receive is from an in-person consultation.   You may benefit from repair of your levator muscle.  Make sure you specifically look at before and after
pictures of real patients who have had this surgery performed by your surgeon
and evaluate their results.  The most important aspect is to find a
surgeon you are comfortable with. I recommend that you seek consultation with a
qualified board-certified plastic surgeon who can evaluate you in person.
Best wishes and good luck.
Richard G. Reish, M.D.
Harvard-trained plastic surgeon