As adjectives, 'fast' and 'quickly' are almost synonyms, and are often interchangeable.
As adjectives, 'fast' and 'quick' are close in meaning, but we use them to refer to different kinds of nouns. 'Fast' tends to refer to speed/velocity, while 'quick' tells you how brief something is. For example, we'd say 'a fast car' or a 'fast road', but 'a quick breakfast' or 'a quick conversation'.
'Swift' is a less common adjective, and it's usually used to say how immediately and efficiently something is achieved. For example, 'Thank you for your swift response.' or 'She made a swift recovery'.