Web-server – One domain, two hosts, multiple subdomains on second host

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.

I just recently did this. See my question. It was kind of a long back and forth, but I did get it set up in the end.

• Set up DNS. The A record will point to your public IP. So, yourdomain.com points to your.pub.ip.add. Add CNAME records for the subdomains. So, sub1.yourdomain.com points to @, and sub2.yourdomain.com points to @, etc. Although the subdomains are all pointing to the same address, the browser will confer to the webserver which subdomain you are trying to reach.

• Set up Apache. You'll want to set up Virtual Hosts for each subdomain (and maybe for primary domain as well). You can define the Virtual Hosts in different places... mine is defined in /etc/apache2/sites-available, and includes the <Location> directive, which is where you'll set up your reverse proxy.