Some people said that there is a secure parking area near border. How really safe is that place? Is there any other recommended safe place for car parking?

Safe enough AFAIK. Well to do Thais going to gamble at the casinos leave their expensive cars there.

It is 100% safe and the resort will even provide shuttle bus service to the border.

Now here is a little dirty secret for you. If you buy 6 or more bottles of booze, the resort will bring it across the border and you can collect it at the parking area.