If my house that I rent is full of black mold is the landlord responsible for paying for a motel while he has the house fixed especially if it takes more then 2 weeks to fix?

Yes  he can be held responsible for this but only if the mold is due to his inaction and if he knew about it or is the apts problem like a leaky pipe before you moved in and he didn t fix it. You may have to take him to small claims court to recoop your costs here but worth it