Almost every Linux distro can run multimedia programs, and has them available in their repository. Several distros are targeted at multimedia production and bundle such software by default. These include Ubuntu Studio, 64 Studio, dyne:bolic, and Musix.
Whichever distro you're most comfortable with.
The Linux kernel supports up to the latest Intel and AMD processors, as well as some other architectures. As such, most programs should run about the same on all of them.
A Linux distribution, known as distro or flavor, is an operating system that uses the Linux Kernel. I think the most common one is Ubuntu.
Yes. The Linux kernel and most programs bundled with it are licensed under the GPL, LGPL,or other similar license that permits commercial redistribution, as long as you make the source code available to your customers. If you want to sell copies of a pre-established Linux distro, make sure that it does not bundle programs that prohibit such activity.
It depends on the Linux you are running. There are thousands of Linux distros. It is possible that your distro wasn't intended to run DVD-ROM. But most Linux will run them.
Depends on the distro, but most use wither bash or sh.
As with any program, installation instructions vary by distro. Most distros should have Pencil in their repository, though, so if you know how to install programs on your distribution, you should be able to install it.
It depends on what distro you are using. Most distros have what is called a "package manager", where you can choose what programs you want to install and remove. In the "Related links" section below is a guide on how to use two of the most common package manager front-ends, Synaptic and Adept. If your front-end is not listed below, or if you want to use the command line, please re-ask your question with the Linux distro you are using specified.
Most modern Linux distributions have a method of updating the system without requiring a clean install. The exact procedure for this varies by distro.
There's Ubuntu, Debian, Red Had, Fedora, Gentoo, Arch, Mint, SuSE, Slackware... A good way to find out is to look into Distro Watch. The web site more or less keeps a monitor on how popular a given Linux distribution is.
There are many different websites that distribute a variety Linux operating systems. The most popular place for desktop distributions computers is Ubuntu.
Linux 2.2 is just a kernel. It does not dictate any sort of user interface, and was used in a large number of distros. I would recommend against using any distro with a 2.2.x kernel, as it is probably quite old and will not support most modern hardware or programs.