Bartholomew is named after Bartholomew Bart, AKA Black Bart. He was a very religious pirate who was actually believed to be a woman. Funny thing? He dressed exactly like Mihawk did.
As for the three admirals, they're based on a child's fairy tale in Japan called "Momotaro", which means "Peach boy". Momo is peach and Taro is a generic Japanese name, like Bob in English. Momotaro, Aokiji, Kizaru, and Akainu ate meat dumplings and gained super strength, which allowed them to defeat the ogres of Oni Island. They became heroes.
In the OP world, that probably refers to devil fruits, and instad of ogres, it was either the giants (suppressing them) Or Gold Roger's Crew.
The Shichibukai are based on the Seven Samurai. I don't know much about that but I'll look into it. They're also based on the Privateers of the Pirate Age on Earth. Sir Francis Drake, Sir Walter Raleigh, Woodes "Gold" Rogers, etc.
And the Yonkou are based on the Chinese legend of the 4 aspects: Genbu the black turtle, Suzaku the Red Phoenix, Seiryu the Blue-green Dragon, and Byakko the White Tiger. In the Chinese myth, there's a 5th, Qilin, or Kirin in Japan, which is basically "The Zero".
Hope that clears up any confusion.