Can my partner drive my novated lease vehicle?

And is my car insured and what happens if they have an accident?

It's your car, so anyone can drive it (with your permission and they hold the relevant license... of course)
If you have underage or inexperienced drivers, your insurance annual premium may increase and should they have an accident, well... there will be a higher excess to pay.
With a novated lease, there isn't a restriction on who can drive your car nor how much private use there is.

A great way to have a newer car for the spouse and reduce the stress of surprise bills.