Hanafuda was a Warlord before the story began Oda revealed in the SBS. He was a smuggler of Ancient Zoans who probably supplied Kaido with a lot of his but the Kaido connection isn't flat out stated. After Hanafuda died Ace was offered a slot but denied it, getting filled by one of the 7 we knew when the story started. I don't think we ever find out who but people smarter than me can probably figure that out

I know that, my point is that on Ace's history page it's stated that he had beaten Hanafuda after joining the WB Pirates, while Draw offered him the position on Sabaody when he met Isuka. Of course, they wouldn't approach a Yonko's subordinate with such an offer.

Why not? If Ace said yes that would've been a crushing blow in the public eye. It would go a long way to showcase the power of the Warlords that pirates would rather be a Warlord than be under the protection of an Emperor. If he said yes the Marines would look unstoppable and hit Whitebeard where it really hurts

Ace traveled aboard Moby Dick after joining the WB Pirates. It's impossible for the Marines to approach him without WB's permission, which he would obviously not give.

I don't remember everything but I do want to point out that what's obvious to us isn't obvious to the Marines. Vaast sections of the Marines think Luffy is an evil mastermind trying to kill people and be brutal. All the Marines would've known of Ace is that he's supremely strong, that he's beaten another Warlord, everything else is word of mouth.

And I don't know enough to know for sure but are we sure Ace beat Hanafuda when he was a Whitebeard Pirate Member or was it maybe before?