Yes, with a Reseller account, (and I'm guessing you are using CPanel/WHM), you get better control of all your sub-accounts, in certain areas, such as changing passwords, setting bandwidth/disk quota limits, and various other features and options.
As for your questions about sub-sub-domains, these are not related to a reseller account, rather, they are DNS questions.
Let me answer your questions 1 by 1:
You can do this without a Reseller account even, by just asking your host's administrator to add an CNAME record to your DNS zone file, as follows:
IN CNAME subdomain.domain.com.
*.subdomain.domain.com. IN CNAME subdomain.domain.com.
*.domain.com. IN CNAME domain.com.
(however the 2nd choice would point all subdomains too... you might not want that).
Sure, and there are many ways to do this, depending on how much control you want to give your user, you can either just create a new whole new account with that subdomain via your WHM, or you can add mail accounts individually to subdomains via your CPanel.
Other higher-end options include setting up your own virtual mail system on the server, but that is a bit more involved.
Could I setup a website without a domain name by using the IP address of the server and a name that I concocted such as http://<_IP_ADDRESS>/concocted_site_name?
Yes. Do it as follows:
1) create an IP-based account via your WHM
2) create subfolders under the site's public_html, e.g. public_html/concocted_site_name1/, public_html/concocted_site_name2/, etc
I hope the above has been of any assistance to you.
And please, never be afraid to ask. That's how one learns.
Only one who stays quiet and doesen't ask is the ignorant one.