Hello!
Welcome to AllDeaf!
BAHA is something that I don't know, and not familiar with. Keep in mind that BAHA and Cochlear Implants are two very different type of implant system.
Cochlear implants -
Length of surgical procedure - it varies. Average is 1 to 3 hours, some are a couple more. For both of mine, it took a little over 3 hours...my surgeon likes to take her time and not rush. Majority of time you go home a few hours after waking up. Depending how well you recover from anesthesia.
Cost of Device - again, it varies to the hospital costs. It is included with the surgical procedure. For both of my surgeries, it was about $46,000 each. I did not have to pay any of it. I think it is on the low end because I went to a teaching hospital. Regardless, I had a very wonderful surgeon.
Cost of Surgery - Up to the discretion of the hospital. Some are under 50k, others are over 100k. Insurance pays for it.
Medicaid should cover all of it, but it can get a bit of a pain in the ass for them to go through the process. At least I read about it. I have medicare so I never had any issues. Someone with Medicaid information should help you out.