I thought it was pronounced like [ɛn] ("e" nasalized), [ɛm] (before "b" or "p"). Apparently, in the end of a word, and before "l" or "ł", "ę" is usually just a lengthened "e". Also, I wish the Duolingo font supported ą, ć, ę, ł, ń, ś, ż, ź. (compare to a, c, e, l, n, s, z)
The possesive pronoun for english "my" depends on gender, quantity and case of the noun that complements in the Polish language.
First of all "pamiętać" (to remember) requires accusative (what or who you remember is the direct object).
Second, the direct object is "my dad" (the construction of these two words is a whole for the sentence's logic matter). After knowing we need accusative for the object direct we take a look at the gender of NOUN which is masculine personal and animate. We as well know that is a singular noun, now we can do the endings.
Finally Acc, masc, animate and personal, singular, 1rst person possesive pronoun forms MOJEGO (which matches the same properties and ending for Genitive case as well, causing your understandable confusion).
Acc, singular for Dad forms Tatę (something I am still yet to comprehend why it acquires the fem ending even tho its a masc word, but someone will explain me one day [please!?])
So mojego tatę is the direct object. All accusative, it looks similar to Dopełniacz (Genitive) but we infer its not Gen because of the context. Also masculine singular nouns end with U (mostly) when in Gen.