You omit it here because there's a possessive (my). The possessive already makes it clear that these are specific/definite apples, which is why the definite article is not necessary in English.
In the sentence about the cats there is no possessive, and so the definite article is required if it is to be a translation of "kattene".
It depends on the gender of the noun. Adjectives have to agree with the noun they describe in terms of gender (masculine/feminine or neuter) and number (singular or plural). So as described in the notes and tips, adjectives (usually) end in -t if they describe a neuter singular noun, have no ending for masculine/feminine singular nouns, and have the ending -e for plural nouns of any gender. For example:
masculine singular: en grønn stol (a green chair) feminine singular: ei grønn bok (a green book) neuter singular: et grønnt bord (a green table) masculine plural: grønne stoler (green chairs) feminine plural: grønne bøker (green books) neuter plural: grønne bord (green tables)