If I remember correctly Spider-Man's Black Suit from Secret Wars. (And might've been based on a female character with a black spider suit, but I can't confirm that to be true.) Both Spider-Man: The Animated Series & Spider-Man 3 never really wanted to delve into the whole Venom origins story so it shouldn't be a surprise that Spider-Man can be cut from that story too.
As far as Venom's powers go it can be simply based off of Venom's obsession with Spider-Man. Like how Carnage is obsessed with the T-1000 stabbing weapons because Carnage is attached to a murderer.
Now let me tell you how Ant-Man's origin makes zero sense without Atom from DC.
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That was just sarcasm about Ant-Man. You don't need DC's Atom in order to tell Ant-Man's story.