The Fritzing pads are connectors... and all connectors do not has solder mask on them so you can solder to them. You would need to replace the Fritzing pads with your own custom pads.
Are your holes not showing up in the gerber view or the Fritzing IDE. In Fritzing, the vias will sometime hide behind other objects... but the holes will still be there and show up in the gerber drill file. You can always send me the .fzz and I can take a look at it.