Regular / Routine // Blood test / Blood work

I would like to expand my vocabulary with some medical terms in English. I have been thinking about how to say, for example, if I go to see a doctor for a blood test.

Q1) Are these my phrases correct?

a) "Tomorrow I will have to see a doctor on an empty stomach to take blood for a REGULAR blood test."

b) "Tomorrow I will have to see a doctor on an empty stomach to take blood for a ROUTINE blood test."

c) "Tomorrow I will have to see a doctor to take blood for a REGULAR FASTING blood test."

d) "Tomorrow I will have to see a doctor to take blood for a ROUTINE FASTING blood test."

Q2) Does the phrase "fasting" can be used instead of "on an empty stomach" as I write it?

Q3) I came across the term "a routine blood-work". Is it another term for "a blood test"?

Thanks