Some nouns can be countable and uncountable. “Fruit” is a common example. “The shop sells a wide variety of fruit/fruits.” “Coffee” is ambiguous, as it could mean a liquid (uncountable), a drink (countable), beans (countable), ground beans (uncountable) or bags of ground beans (countable).

The first one means the coffee itself - different beans, e.g., Columbian, Ethiopian, arabica, robusta, etc. The second one refers to the styles of coffee - espresso, cortado, macchiato, cappuccino, etc.

No difference, although 1# is preferred.

Both words "variety" and "coffee" have a variety of meanings that makes it impossible to pin down the meaning of either sentence to just one choice. "Variety" can mean a subtype of a species. For example, a dog is a variety of mammal. "Variety" can also mean an abundance of variation. For example, a singer can sing a variety of songs. "Coffee" can be a drink, a biological category, a subtype of that category, or just the general idea of all of those things. For instance, when we say "I like coffee" we do not intend the word to have a meaning so precise. The person who says he loves coffee may detest the vast majority of coffees. Hence, I don't know the answer to your question. The first seems to say Starbucks offers just one type of bean, but nobody would interpret it that way. The second seems to make sense but to be totally false. Starbucks does NOT offer a variety of coffees. They do, however, offer a variety of coffee drinks.