If you're enrolled in an HDHP for the whole year, you can add the entire catch-up amount regardless of where your birthday falls within the year.
If you had HDHP coverage for only part of the year, you have to prorate the catch-up amount.
Once you turn 65 years of age, your Health Savings Account is freed up substantially. You are free to spend your HSA funds on whatever you want, not just qualified medical expenses. Note that any distribution for non qualified medical expenses will be taxed (just like ordinary income), but at least you are getting the funds out of your HSA.