Vickie,
I would recommend you go to the social security office and ask some very specific questions regarding benefits. You mention you started his social security in December. Assuming you took the option of getting social security retirement, his benefits would have been reduced by as much as 25%-30% because he was not 65. However, if you really applied for social security disability insurance, your father would have received a higher amount which would be equal to retirement at 65. The stipulation is that the disability either lasted for at least a year or was expected to last at least a year. Supplemental security income, on the other hand, is based on financial need and would be in addition to disability insurance.
You asked about medicare being automatic with disability. Medicare is typically given after two years of disability. If the doctor states that he/she does not believe the patient will ever recover (i.e. terminal diagnosis) there are exceptions. Usually state programs kick in sooner but are often limited to not owning a house or other assets.
Applying for benefits on-line is sometimes more difficult than going in person and asking all the questions you need during the process. It sounds like your father filed for early retirement and has reduced benefits and if this is the case, you want to lobby hard to get his status changed over to disabled.
When trying to qualify/sign up for disability, it can be especially trying and three are so many things to take into consideration. There may be a social worker available where your father is receiving his medical care and they may be able to help you navigate the maze. I hate to give you specific answers as I am not familiar with the particulars surrounding your father.
I hope this helps you somewhat.
Ed