No, it's the default word for "towel". It could be a hand towel, a regular towel, or a beach towel.
"The lass" is an accepted regional variant, but our default translation is "the girl".
I think i can answer that one: føner relates to using an electric appliance -literally 'dry with air' (usually with hair, but also on public toilets for hands). Tørker on the other side relates to a manual drying