If I am a signer on my Mom’s account can Medicare take 100% or 50% of her money?

Because each joint signer is entitled to take out 100%, Medicaid will regard the money as being 100% that of whoever applies.  Be careful about putting money into your mother's account as Medicaid will regard it as hers.  Be careful about taking money out of your mother's account as Medicaid may regard it as a transfer/gift in an attempt to qualify for Medicaid (by hiding her money) and penalize her, not paying for her care for a period of time.