New Cat

Hi,
I just yesterday found a stray cat wondering around my neighborhood. My family has always wanted a cat so we decided to take him in. He is a great cat but I have just a few worries.
1. My dog is the most docile creature you would ever meet. A robber could come in and she would love it . However, my new cat, Hobie, seems to loathe my dog. How long will it be until they're comfortable with eachother,
if they ever are.
2. Since my cat was a stray,I am worried that if I let her out, she will run away for good. What should I do? We do nothing but pamper her here but I am still worried.

Thanks