Short answers: Q1 Yes, Q2 No
Long answer: You can renew your medical whenever you’d like. But if you do it outside the window (either 28 days, 30 days or one calendar month, I just can’t remember sorry) before the expiry of your current medial, your new expiry date, will be the date 12 months from the date you did your medical. Whereas if you do it within the window, you keep your anniversary date, so a 12 month extension to your original expiry.