"Handsomeness" is a subjective term. They might mean it, even if most other people don't feel the same.
They also might not mean it, and just see it as a nice thing to say.
If you want to see how differently people view looks in Thailand, just look at something like Miss Thailand. Skinny and very pasty women. Or "pretties" with orange hair, bleached skin, huge contacts and braces. Not attractive at all.
Probably not. Thai people will tell a foreigner they're handsome even if they're with their partner, they'll tell their partner they think a foreigner is handsome, or the male partner will tell a foreigner they are handsome.