When will the first people born in 2000 reach old age?

Depends on what you consider "old age". That's subjective. They'll hit (traditional) retirement age when they reach 65, but many will retire before or after that age. That's also the traditional age people begin drawing Social Security (in the US, although waiting until they are older allows them to draw more money) and having Medicare available for their health insurance.

2065 ?

In the year 2060.

2065 (65 is usually considered the start of old age)