komórkę is singular accusative/biernik komórki is singular genitive/dopełniacz=plural nominative/mianownik=plural accusative/biernik=plural vocative/wołacz.
MA is followed by accusative,
SZUKAM is followed by genitive,
accusative is the most common case for direct object, but genitive happens a lot, some instrumental and dative. there is a list somewhere in the forum, of the most common genitive verbs, I will try to link