Right... notary is about authentication .. user is the person who claims himself to be [done using a picture id, say].
It would be really useful to have this process done online so that it can avoid a trip to a notary public office (and pay the $10 or so fee).
The problem is not easy to solve.. but a central agency (a e-notary service) could potentially use a remote system like webcam or voice to verify you. It needs to be robust that someone can't easily impersonate. [likely use a live-person on the other end and may be use your biometrics like iris-scan to confirm it's you]

I see still for some financial transactions.. while 99% of work can be finished online (read: without leaving your home), a last bit still needs a notary.. if this task can be done online, it will be nice as you can instantly finish up some financial transactions (e.g you do an asset transfer to another person online with your finanical institute)

Typing fast may not be the concern; programmers need to spend more time thinking than producing typed output. Using all fingers helps reduce the risk of muscle damage compared to using only two or three fingers (like carpal tunnel syndrome). Also keeping head straight looking at the screen rather than looking down and up can reduce stress on the neck muscles. I would say the benefit to our physical health outweighs more than any other efficiency in support of touch typing.