And if so, how did they differentiate between male, female or neuter nouns? Did English ever have gender-specific (in)definite articles? (like der/die/das in German)
Yes to all of your questions: Old English had three genders, each of which had their own definite articles and case endings (though the masculine and neuter were largely the same).
If you look at the Wikipedia article on Old English Declensions, you can see sample declensions for masculine, feminine, and neuter nouns in their five cases, as well as examples of the definite articles. This system had fallen out of use by the time of the earliest Middle English writing (in the 15th century), and no trace of grammatical gender survives today outside of the personal pronouns.