Good luck!
Buying a card privately is a nightmare....
1st - Do you plan to finance the car through a bank? If so, they will only lend you 80% (from memory - could be different) of THEIR valuation of the vehicle. Unless you are a PR or Singaporean, you will also have to have a local guarantor to secure the loan.
When we bought our car, the previous owner had to come into DBS with us to fill in paperwork for our loan!
You also need to to insure the car (even though it wont be in your name yet) prior to the loan being given.
Transfer of rego requires that BOTH parties go to the LTA and do the paperwork - the price wasn't that expensive.
The PARF value should be listed on the rego or COE papers, but I'm not sure about how to scrap the car.
In hindsight - it would have been much easier to buy a car from a reputable 2nd hand dealer (if they exist!!)
Good luck! and do your homework!!