• If you are paying his medical costs, you could claim him as an "additional dependant over 18" and claim medical expenses. (This credit is separate from your own families medical expenses and expenses must exceed 3% of your father's net income).

• If your father qualifies as "infirm" you could claim the Canada Caregiver Credit - CCC (this credit used to be available for parents over age 65 regardless of health or infirmity). More information about claiming the CCC can be found in this link to the CRA guide: https://bit.ly/2PPh21L
• If your father qualifies for the Disability Tax Credit (DTC), any of this credit that he does not need to use may be able to be transferred to you. This credit needs to have a T2201 form completed by an authorized practitioner and must specify that the credit is being transferred to you. More information in this CRA link: https://bit.ly/2yNovKZ 

He's not designated as "infirm" but I wouldn't be comfortable with him living alone. I have him on my employee health benefits and pay extra for that. Can I claim that? If so how? Can I claim the caregiver amount for previous years before the legislation changed to"infirm"? If so how?

I would suggest contacting CRA in regards to claiming the Caregiver Credit for the years prior to 2017 when any parent over 65 qualified. If they will allow you will need to make "adjustments" to each year's tax return.