Just to clarify... being 'familiar' with a country means you know your way around geographically and culturally.
When you know a person you have to use the personal a. But not with things like countries
Because personal a is also used for moving. Example Yo voy a mi casa. I am going to my home/house. And here you don't go anywhere, so it's out. Also personal a is used for persons. Example Yo veo a Luís. I see Luís.
If you're talking about a movement to a place, that a is not the "personal a" anymore.
This is a strange sentence. "My parents know Germany well" would sound more natural.
Not necessarily. I could say 'I know math.' Same sentence structure... same idea. Besides, this sentence says they only know Germany... but not necessarily 'bien'.
Alemania is the name of the country (notice that it's always capitalised), and alemán would be the adjective and the name of the language (usually spelt in lowercase).