Pardon me for asking stupid question, kinda noob in this, but
what you meant for premium and excess is it,
Insurance premium is that something I have to pay yearly,
and;
Excess is that something like, I have to fork out from my own
pocket in accident or something right?
But if let's say, my family car (dad's car), insurance cover
both my parents, I'm still allow to drive alone right? But when
getting into accident, it won't cover me right? 
No worry..
Yes, if you own the car, you have to pay an insurance premium
yearly, and a road tax (6 monthly or yearly, depending on your
budget). Your insurance and road tax starts from the day your car
gets registered at LTA.
Right, Let's say excess is 1.5k. You kena accident (touchwood)
and repair cost is 2k. You have to come up with the
first 1.5k and the rest covered by insurance
company.
For your family car, you have to check with your dad. They
usually cover the main driver, 2nd driver and "all the drivers
authorized by the owner of the car". But there is a catch here:
"Additional Excess of $1000 - $3000 applies to young and
inexperienced drivers: i.e. 26 years old and below, driving
experience of less than 2 or 3 years"
Means if you are the one driving the car at the time of
accident. the excess will be
$1500 + $3000 = $4,500
If your repair cost is only $2k, means you
cannot claim insurance..