How can someone get a VA disability rating years after leaving the service and also get VA healthcare in the Philippines?

To your first question, can he get a disability determination so many years after he left the military service? Absolutely. There is no "statute of limitations" on applying for a disability determination. Assuming he is granted one, the worst thing that will happen is that the date of determination will be the date that the application was submitted.

In order to show a service connection for a illness or injury, you'll have to show that the military was the direct or indirect cause of the condition and that he was in the service at the time. For presumptive conditions (which assume the military service caused the issue), you'll need to show that you were at the location specified, at the time specified and that you were in the service at the time.

To your second question. If your father has a cumulative disability determination of 50% or more, then all healthcare can be treated at the VA clinic. If it is less than 50% then those service connected conditions can be treated at the VA clinic. You won't be charged for any of the eligible treatment in these situations (all if over 50% or service connected if less).

Another way is to enroll in VA health care if your determination is less than 50% (or you don't have one yet). The "priority group"* is dependent on different factors and will determine copays, costs, availability, etc. Most* veterans are eligible to enroll in VA health care, regardless if they have service connect illnesses or injuries.

The very first thing your father should do is contact a Veteran Service Organization (i.e., DAV, VFW, American Legion, etc) and submit a claim. They will be able to walk him through the process, see if there are any conditions he may have that fall into the 'presumptive' category, etc.
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* VA Health Care eligibility - https://www.va.gov/health-care/eligibility/
* https://www.va.gov/health-care/eligibility/priority-groups/

The short answer is yes. If he can document that he has an injury or condition linked to his service time, he can get an determination. Any Veteran can use VA health care, the disability rating just makes a difference in what priority category you land.
If he retired, isn't he on Tri-care for Life?
I didn't apply to VA until I was 65 (hearing). Luckily I had copies of my last Hearing Evaluation and a copy of my DA Waiver. I still have a Medicare Advantage Plan. Any non-service stuff get billed back to Anthem, but it generally saves me Out of Pocket.
I use DAV as my VSO. I've been happy with them.