Numeric subdomain

Is it possible to create such multi level sub domains?

Yes. You can have as many levels as you like in DNS.

is this based on the hosting company?

Your host might limit what you are able to do.

Isn't sub2.sub1.subdomain a different subdomain rather than a sub domain of sub1?

That isn't a useful distinction.

Will all of these subdomains have their own doc roots?

Assuming that all the subdomains end up resolving to the same IP address (and they really don't have to):

Browsers will send the FQDN in the Host header. How the webserver handles that depends on the webserver.

You can configure a separate Document Root for each — and you should (to avoid duplicate content penalties in search engines), unless you are going to do stuff to dynamically determine the content based on the FQDN.

How will I handle users coming with and without www.

However you like. www is only another subdomain without any special properties (other than convention). It is widely considered to be a good idea to pick either "with www" or "without www" as your canonical primary site and redirect the other one to it.

Responding in an answer for the upvote ;) . I don't know off hand how bind9 does it, normally it should first check it's views (in configured order) to decide if it should act as a resolver or authorative. I agree with you that it should have acted in resolver mode in your case (assuming that other queries (like www.google.com) worked) and then answered from auth mode, but apparently it didn't. That's why I always use a dedicated resolver when I test this stuff.

Your solution is only a partial one, you never test if this works also from the outside. It's a "short-cut" for your tests saying "also ask this one if you don't get an answer".