Renting with no lease in Florida?

My mother was renting a house for about a year and a half, she was moving out and asked the landlord if I could take over the payments. He agreed under the cirstances that I would inherit her security deposit and pay an additional $200 plus an extra $25 a month. I was weary but I needed a place and fast. we have lives here for two weeks now and he has niether brought a lease nor collected the rent. He showed up with a rental/credit application and asked me to fill it out. Im concerned because if he doesnt like what he sees on my credit he may not want to rent it to me. What should I do? we are already moved and and dont have money to move to a new place? if he says he doesnt want us to stay should we make him evict us and handle it in court or will it be useless since we dont have a lease?