If you could count stars at a rate of about one per second, how long would it take to count all the stars in the milky way galaxy?

It could take several thousands of years.

Explanation:

To be specific, the exact number of stars in the galaxy is unknown, it's estimated to have around 100 to 400 billion stars.

But for the sake of this test, let's take as valid a recent study of the European space agency, that believes that we have 100 billion stars orbiting our galaxy.

If you could count 1 every second it would mean you'll need at least 100 billion seconds to do it. How many days is that?

We have:

100 billion seconds = 1.666 billion minutes

1.666 billion minutes = 27.777 million hours

27.777 million hours = 1,157 million days = 3,170 years.

You would need at least, 3170 years of spare time, considering that you will do no other thing than counting stars for the next 3 millennia.