He's just DMC Dante but with Vergil hair styling.
Lore answer is he was never trained properly and cooks his skin every time he does magecraft.
>>280867535
He has more than 1 circuit, he was just never taught how to use them properly.
The reason he is able to summon swords and stuff is because of how he was saved from the fire by Kiritsugu implanting Avalon in Shirou to give him some healing hax, unintentionally also caused both his Element and Origin to become: Sword. On a conceptual level he is united with mythological weaponry.
>how was he able to beat/copy Hercules and gilgamesh
Something something Unlimited Blade Works lets him copy the abilities of the weapons' original users.