I worked in restaurants for 6 years before I graduated from college. Yes it is true, if your tips + $2 something per hour doesn’t equal minimum wage you will get paid more hourly.

A lot of States (or maybe cities) have much much higher minimum wages for servers than my state. California, Las Vegas, and maybe New York pay higher than the $2.

Yes it is. See a link from the Department of Labor below.

https://webapps.dol.gov/elaws/faq/esa/flsa/002.htm

It's true, but not all employers track this or are willing to pay it unless forced.