I am busy playing pc game?

The second is fine, but the first needs "a" or "the" before "pc" and the third needs either of the same before "sofa." These are not phrases, but sentences. The words after the verb explain what one is busy with for the first and comfortable with for the other two.

a game, or plural games to indicate the generic idea.  sitting on a sofa, or sitting on sofas (generic idea). You could also employ the (the game, the sofa) if you meant a very particular and specific one.

English cannot be "generic or specific".  A language can, the English Language can be, but "English" is an adjective, really, and not subject to plural or articles, and even when used as a noun, it is, as a proper noun, by definition specific.  You cannot have a generic proper noun, the proper part declares it is specific to some particular thing, a name for that thing.

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Adjectives qualify the nouns. Adjectives qualify verbs or adverbs; look for 'ly' endings to words. Use the indefinite article 'a' after the word 'playing'.