Start by reading the Derivative Distro Howto.
You can certainly make a distribution based on Ubuntu, and as far as I know there is no specific restriction on the live CD, so you can make derivative works based on it.
The code isn't be a problem: as far as I know it's all freely redistribuable software, Ubuntu doesn't have any specific rights to distribute that you don't also have. But the branding — trademarks and artwork — might be. The obvious thing you should check is what you may do with the Ubuntu artwork, and how you're allowed to use the name (it's trademarked).
A typical example of artwork and trademark-related limitation is the Iceweasel saga. The Mozilla foundation wants only “acceptable” derivatives of Firefox to have the Firefox brand, so even though the software is free software (as in free speech), the branding is not. Although the Mozilla foundation was prepared to trust Debian to make only acceptable changes, such as security fixes, they were not willing to extend that trust to others. But the Debian Free Software Guidelines specify that the “license must not be specific to Debian”, so that people in your position know that they can make derivatives. Since no acceptable compromise was found, Debian does not distribute “Firefox”, it distributes “Iceweasel” with the same code and different branding.
Ubuntu is less strict on that point, so if you want to make a derivative, you do have to check whether you may retain the branding on any component you change (starting with the distribution as a whole).
Absolutely you can do this. Many companies all over the world run a portion (sometimes all) of their commercial infrastructure on Linux distributions. Ubuntu in this sense is no different from Red Hat, Debian, SUSE, and the rest.
Just because the kernel and many system components are under the GPL, that in no way means the code you run on top of it must also be free or open source software. A simple search for commercial software and commercial web services that run on Linux will prove this quickly.
One simple example would be Google. Virtually their entire server infrastructure runs on Linux, but clearly that hasn't forced them to give out the code to their web indexing software, or Gmail, or G+ (not to mention the entire Android platform which runs on Linux).
As for being sure enough to convince your legal department that it is ok to run Ubuntu Server, you might consider buying an Ubuntu Advantage support contract from Canonical. They (ok, we) include legal indemnification with each support contract. Please see:
http://www.canonical.com/enterprise-services/ubuntu-advantage/assurance-terms
http://www.canonical.com/enterprise-services/ubuntu-advantage/overview
Also: I didn't mention EC2 specifically because there is no reason to think that hosting it on EC2 would be any different compared with running it "in house" from a legal standpoint.
Also, too: In the case of Android, let me clarify. Android's modifications to the Linux kernel are GPL'd, however the rest of the platform is on a very permissive Apache-style license, and obviously a great many companies sell paid, closed-source software that runs on it.
Best Answer
disclaimer: I am not a lawyer
An excerpt from
/usr/share/doc/humanity-icon-theme/copyright:So, the work uses the GPL version 2 license. AFAIK, this means that you can use it freely providing you've put a note in your program that you're using the Humanity Icon Theme which use the GPLv2 license.