The infill portion of your model is configured during the Simplify3D process. After loading your STL file into S3D, edit the process and examine the Infill tab and Infill slider. You'll see a percentage indicator, as well as an extruder selection (left or right, if you have two) to be used for the infill. There are other options within the configuration that would have little to no effect on the problem you are experiencing.
Once you have checked and corrected the settings as needed, used the prepare-to-print option and press the play button for a preview to see the infill being printed before you send it to the printer.
100% infill is impractical, and one can create strong models with as low as 20% infill.
Infill is used to save filament, as you suggest, but it is also used to provide support for top layers on areas that are not vertical. Sometimes, one would use a higher infill figure to provide for smoother top surfaces although increasing the layer count for top/bottom can accomplish that.
Check your top/bottom layer figure in the layers tab to ensure you have a reasonable figure. Three or four layers are good for cosmetic reasons, more if you need additional strength. Anything higher or absurdly high would cause some of the trouble you describe.