Do you need a motorcycle endorsement and motor vehicle insurance for a vespa scooter with a maximum mph of 45?

Very likely yes. Some states say if it is motor driven by anything, then you must have both. Some states say 30 cc or more. Check with your DMV, they will be glad to tell you.

But I'm positive a Vespa must have both in all states. They are not permitted on any Interstate though.

if you drive it on the street yes (u.s.)

Depends where you live,,,in Canada for instance,,you need insurance,,,but you don't need a special classification of license to ride a bike that small.
Just a class five which is for automobiles.

Yes. And stay off the freeways and interstates with it.

You don't need a motorcycle endorsement or insurance in Washington State,but your state might be different.