Yes Scaling is one of the steps by which the stains can be removed. Some stains are extrinsic meaning present on the outer surface due to deposition of plaque and calculus etc and some stains are intrinsic meaning they are due to staining is present internally which can be reduced by dental bleaching.

There are two type of stains.  Intrinsic stains which is from inside the tooth cannot be removed by scaling. Bleaching can be done for mild intrinsic yellow stains. For extrinsic stains due to tobacco or food can be removed by Scaling. The cost depends on the clinic and doctor. I usually charge 1.2k for one seating.

Depends on the type of stain which can be determined upon physical examination only.You are requested to visit Dentist

Well there are types of stains. If the stains are intrinsic then scaling might not work. If you want teeth whitening then there's another procedure for that which is bleaching of teeth, And yet if the tooth discoloration is much deeper for that veneering has to be done. As per scaling may cost you around 1k to 1.2k and timing depends of how much plaque and calculus have been accumulated there.