How do declensions correspond to gender?
There is no direct correlation, but most second declension nouns are masculine or neuter and most first declension nouns are feminine. (There are exceptions, especially there are many masculine nouns that are first declension, like μαθητής.)
The third declension has an even mix of masculine and feminine nouns.
What is the mnemonic for the first declension endings?
“Asina Ionisas” (ασινα ιωνισας)
Nominative (and vocative), feminine, singular ending(s) of the first declension
-α / -η
Genitive, feminine, singular ending(s) of the first declension
-ας / -ης
Dative, feminine, singular ending(s) of the first declension
-ᾳ / -ῃ
Accusative, feminine, singular ending(s) of the first declension
-αν / -ην
Nominative, feminine, plural ending(s) of the first declension
-αι
Genitive, feminine, plural ending(s) of the first declension
-ων
Dative, feminine, plural ending(s) of the first declension
-αις
Accusative, feminine, plural ending(s) of the first declension
-ας
Nominative (and vocative), masculine, singular ending(s) of the first declension
-ης / -ας
Genitive, masculine, singular ending(s) of the first declension
-ου
Dative, masculine, singular ending(s) of the first declension
-ῃ / -ᾳ
Accusative, masculine, singular ending(s) of the first declension
-ην / -αν
Nominative, masculine, plural ending(s) of the first declension
-αι
Genitive, masculine, plural ending(s) of the first declension
-ων
Dative, masculine, plural ending(s) of the first declension
-αις
Accusative, masculine, plural ending(s) of the first declension
-ας