First, is the the focus switch on the front of the camera set to "M", or Manual? As you are looking at the front of the camera, this switch is down and to the right of the lens. This needs to be in either "S" or "C" (Single or Continuous) in order for the lens to Auto Focus. I have found that it is very easy to move this lever inadvertently.
Regarding the dust specks. Probably just on the mirror, the prism, or the focusing screen. None of these will make a bit of difference on the image on film, just what you are seeing in the viewfinder. Cleaning the mirror and the bottom of the focusing screen is pretty straight forward once you remove the lens. Just try using a air blower or soft lens brush to remove any lint or dust. Your use of the term sensor is incorrect in a film camera, the film is the sensor and you install a brand new one with each roll of film. :-)
I bought a F100 a couple of months ago and love it. Welcome to APUG and to film.