Would an actuary be confused about what prime numbers are?
Actuaries must go through college and rigorous studies in mathematics to obtain their jobs. Prime numbers are introduced in basic high school mathematics.
The answer is no.

Are Doctors of Homeopathy more likely than Doctors of Internal Medicine to recommend Quartz as a treatment?
Doctors of Homeopathy are practitioners of "alternative medicine". In alternative medicine practices, Quartz is believed to have powers. Doctors of Internal Medicine have completed a medical residency and do not recommend alternative medicine.
The answer is yes.

Is the title of Shirley Bassey's 1971 diamond song a true statement?
Shirley Bassey recorded the song Diamonds are Forever in 1971,. Over time, diamonds degrade and turn into graphite. Graphite is the same chemical composition found in pencils.
The answer is no.

Does parsley sink in milk?
Items sink if they are denser than the surrounding material. Parsley has a density of 0.26 g/cm^3 when fresh. Milk has a density of 1.026 g/cm^3.
The answer is no.