Is it true that appetite suppressants are drugs?

Yes. Any chemical that you take into your body that produces a change in the way your body functions (for good or for ill) is, be definition, a drug. Government regulations may group things into "drug" and "non-drug" categories for regulatory purposes but they are still drugs. Herbal and dietary supplements can have a huge impact on the drugs your doc is prescribing so please tell them everything!
Yes. However the real question is whether you have a net benefit to your health when you user them. A ten percent weight loss will have a huge benefit and current regimens do better than that.