Well I think it's based on how they fight. Madara fights with chakra and genjutsu: no DNA transfer. Hashi fights by stabbing you with a big piece of wood: possible DNA transfer.
I don't think so, two different and opposing personalities who didn't share anything in common other tha being descendants of the SO6P.
Besides he knew he could beat Madara, he had no need to resort to sneaky plans.Also, he thought Madara died during their last battle, so he must have been under the impression that peace was coming finally after defeating the biggest threat at the time.
Of course Hashi had more powers than we currently know, little about him has been shown other than him being ablr to top Madara, considering how powerful Madara was(most powerful Uchiha by many accounts) Hashi had to be able to counter any and all of EMS techs.
But it's highly unlikely that he stole Madara's Dna to obtain it.