I have a question... how will I write this as a journal entry
If Jan was starting her business on jan 1st and jan is only doing journal entries from jan 1st to jan 31st.

Jan will receive a salary of $2,000 on both the first and fifteenth of each month. Payment on the fifteenth is for service to CSC from the first to fifteenth of the current month; pay on the first day of a month is for service in the prior month, from the sixteenth to the end of month, irrespective of the number of days.

Would it be

Debit credit
Cash $2000
Service revenue $2000??

Or would it be $4000? Or a different number?

A salary is not revenue to the business.

On Jan 15, the JE would be:

Dr. Wages Expense 2,000
Cr. Cash 2,000

On Jan 31, the JE would be:
Dr. Wages Expense 2,000
Cr. Wages PAYABLE 2,000

It is wages payable as the payment does not occur until Feb 1 but it is for employment skills rendered to the business between Jan 16 and Jan 31