First: Can Pokémon in hidden grottos have non-hidden abilities?
Second: Does the "Met at" location mention that the Pokémon was caught in the grotto, or does it just say the Route the grotto is located on?
Thank you in advance.
Can Pokémon in hidden grottos have non-hidden abilities?
No.
Hidden Ability (Bulbapedia)
Does the "Met at" location mention that the Pokémon was caught in the grotto, or does it just say the Route the grotto is located on?
The Pokemon's met location will display as "Hidden Grotto" and not mention the route at all. Below is a Dunsparce I caught as proof—please excuse the poor image quality.