I have a guess. A previous lesson mentioned how "en" can be used to replace "de" + "a noun." For example:
As-tu des pommes? - Do you have apples? Oui, j'en ai. - Yes, I have some.
"En" replaces "des pommes" there to be translated as "some." I'm assuming something similar is happening here and we just don't know what it's replacing because we don't know the full conversation.
Edit: As for why it doesn't accept le/la in place of en, I don't know.
According to https://www.frenchtoday.com/blog/french-grammar/how-to-use-the-pronoun-en-in-french, en replaces a thing Introduced by a verb followed by “de, du, de la, de l’, des” ("se souvenir de ..." in this case).
As a Finn, sentences like these trip me out, so much of what feels like "clutter" in here; repetition of "redundant" pronouns and grammatically mandated pronouns/prepositions sometimes seemingly pointing 'nowhere' within the sentence.
(For reference, in Finnish this phrase would be expressed with three words.)
With phrases like these, just gotta hammer them in through merciless repetition.
Because both nous are not the same.
The verb here is reflexive, it's "se souvenir". It is conjugated in this way :
1st person singular : me souviens
2nd person singular : te souviens
3nd person singular : se souvient
1st person plural : nous souvenons
2nd person plural : vous souvenez
3nd person plural : se souviennent
But this is just how you conjugate the verb. You need a subject, there it's 1st person plural so it's nous. Then if you conjugate "se souvenir" at the 1st person of plural, it's "nous nous souvenons" (the 1st one is subject, the second one is part of the verb). There the sentence is negative so you have to put "ne" before the verb and "pas" after and finally you have "nous ne nous souvenons pas".