3) What is the duration of Doctor Neggistential's Workbench?
The event, will run from April 12th through April 23rd. You can participate any time within that period by visiting Doctor Neggistential's Workbench page with your Mechanical Negg and a Kit that suits it.
So yes you can buy on the 23rd and still receive the bonus prize for each tinker kit.
There's no final bonus prize for the NC part if that's what you mean.
As for the negg hunt as long as you have the gold marks you will receive the "best" prizes after the event.
Hope for a new avatar.