Need to know if this is mold or not
Yes, it's mold. This happened in my apartment after an extended stay away from home during the summer. I used plain old soap and water and it has worked for me. I had no problems doing it this way. There is no way to indefinitely get rid of all the mold (you will inevitably leave some mold spores behind) as long as there is enough moisture in the air. 

There are many ways to prevent mold growth. I bought a dehumidifier and it seems to have done the trick. I have not had any mold since. No mold will grow without moisture. Get rid of the moisture and you will get rid of the mold. 

Update 
I found an article that does a good job explaining how to get rid of mold.