At what age can one continue working part time and still draw SS?

Here's another tidbit from ssa.gov;
You can get Social Security retirement benefits and work at the same time. However, if you are younger than full retirement age and make more than the yearly earnings limit, we will reduce your benefit. Starting with the month you reach full retirement age, we will not reduce your benefits no matter how much you earn.

We use the following earnings limits to reduce your benefits:
If you are under full retirement age for the entire year, we deduct $1 from your benefit payments for every $2 you earn above the annual limit.
For 2018 that limit is $17,040.

In the year you reach full retirement age, we deduct $1 in benefits for every $3 you earn above a different limit, but we only count earnings before the month you reach your full retirement age.
If you will reach full retirement age in 2018, the limit on your earnings for the months before full retirement age is $45,360.

Starting with the month you reach full retirement age, you can get your benefits with no limit on your earnings.

I was 62 and was allowed to make 14k a year without penalty. My husband was born in 1947. 66 was full retirement age and he was allowed after 2 months to earn as much as he wanted without penalty.
Like said, it now depends on when you were born for full retirement age.

Also from the ssa.gov website;
Retirement Age Calculator
The Full Retirement Age Is Increasing. Full retirement age (also called "normal retirement age") had been 65 for many years. However, beginning with people born in 1938 or later, that age gradually increases until it reaches 67 for people born after 1959.

The 1983 Social Security Amendments included a provision for raising the full retirement age beginning with people born in 1938 or later. Congress cited improvements in the health of older people and increases in average life expectancy as primary reasons for increasing the normal retirement age.

If you were born on January 1st of any year you should refer to the previous year.
If you were born in: (choose year)
Your full retirement age is; (push for Calculator)

The earliest a person can start receiving Social Security retirement benefits will remain at age 62.

From ssa.gov;
You can get Social Security retirement benefits and work at the same time. However, if you are younger than full retirement age and make more than the yearly earnings limit, we will reduce your benefit. Starting with the month you reach full retirement age, we will not reduce your benefits no matter how much you earn. Mar 17, 2014
--------------------------------------------------------------
(me) Please note that "full retirement age" is no longer 65 for everyone. You would need to check what your age would need to be to collect full benefits. 
Mine is 66-1/2 years old because I was born in 1957. It goes by the year you were born. 

As far as I know, you still get Medicare (health insurance) at 65.