They are equivalent. I can't speak for American English but certainly in British Engiish the verb 'have' is used an enormous amount (have a beer, have a bath, have an argument, have a nap, have a go (attempt), have a good time) and the first sentence would probably be used slightly more. Nothing wrong with (machachi's corrected) second sentence though.
Yes, they mean the same and "My father often eats beef" is clear.
I think there's a note to be made as "My father often has beef" would have clear meaning when the topic of eating, food likes or dislikes, has been established. If you started a conversation with "My father often has beef" the listener would probably feel the need to clarify "What, to eat?" because the verb 'to eat' isn't there.
We also say "My father likes/loves his beef." which you can assume he has it often if he likes it so much.
Unless the context was very specific, 'my father has beef' would sound unclear.
All sentences are possible, though (b) sounds more as if the quantity of beef is being discussed - e.g., you are at a barbecue and are getting a plate of food for your father. You ask the server to put a lot of beef on the plate because 'my father has a lot of beef'.