you apply for uni when you are in your third year. There is an
application date you just apply. You will graduate at age 19, so
you will start your uni at 20-21y.o. and then graduation at 23-24
years old.
Go NTU, you can skip semesters, 1 or 2 semesters but it depends
on your poly results. Dip with merit would definitely get you a
year off your 4 year uni course.
Go NUS, you exempted from 5 elective modules (for all poly
students). Therefore that is equivalent to a semester, but it
depends on yourself if you wanna spread your remaining modules over
the 8 semesters (more slack) or 7 semesters (more xiong).
Go SMU or SIM... I dont know.