What if I'm taking other subjects as a school candidate but not
bio? Does that mean I will be both a school and private candidate?
For example, I'm taking the subject English as a school candidate
and taking Biology as a private candidate. Is that possible? and if
I take Biology privately, will it affect the school's ranking?
It doesn't matter what subjects you're taking. In one year, you
can be EITHER a school candidate OR a private candidate,
not both.
So as far as MOE/SEAB/Cambridge is concerned, there's no such
thing as taking one subject privately and other subjects in
school.
Your only hope is to (get your parents to) convince your HOD and
principal to let you register for your Bio papers together with
your other subjects (ie. you take Bio in your own school exam
hall), and you study the subject yourself for the rest of the year
(since the school won't let you attend their Bio classes).