Question on toilet mounting; No visible bolts?
Many toilets are held in place around their bases with silicone sealant only these days, especially if the cistern is fastened to the wall. 

No toilet I have ever seen (in 30 years in trade) is mounted directly from underneath i.e. accessed from under the floor). 

Many modern toilets have a pair of plastic multiholed brackets that are screwed to the floor, the toilet drops over these and screws through the side of the pan hold it in place. Silicone sealant is still advised. 

Older toilets screwed directly through the pan base into the floor.

Anyone seen anything else?