زَيْدٍ: proper name, but fully declinable; genitive kasra.
الرَّجُلِ: definite with al-, not a diptote for that reason; genitive kasra.
أَحْمَدَ: proper name with verb-like pattern; diptote; genitive fatḥa.
هَذَا: definite demonstrative but indeclinable; its syntactic position determines its case.
For each word ask: type of definiteness? declension class? syntactic function and marker?