Is MOSFET gate threshold voltage a limit or minimal "Full-on" switching voltage?
The gate-source threshold voltage is the voltage that is required to conduct (usually) 100 uA of current into the drain. Different MOSFETs have different definitions and some devices define the threshold voltage at up to 1 mA drain current.

It's a fairly useful comparitive indicator of how a certain device might operate when given a proper logic level signal but it's always best to examine the data sheet. Typical you might find this: -



You can see V\$_{GST}\$ causes very little current to flow but raising the gate voltage above this you'll see that the device conducts far more current.

Usually, maximum rated voltages for MOSFET gates is +/- 20V and so there is a fair bit of margin between operate and damage levels.