1. Yes, some files can install themselves. Even the ones that don't install themselves are not hard to install once you know how.
2. You can use KPackage from the K menu in the System section. It can do some package installation and removal. Synaptic is another popular graphical front end. Real men use aptitude in a terminal. You can also install software by just typing:
apt-get install the-software-you want
Apt-get is used in a terminal to add or remove software. You use "apt-get install whatever" or "apt-get remove whatever". The downside to apt-get is you have to know the name of what you want to install, so you can't browse with it.
3. "apt-get update" will update your list of packages that are available according to your list of package sources. I think kpackage does this also, but I'm not sure since I use aptitude. So yes, there is are several tools to update. Try kpackage, or synaptic, or aptitude.
4. Yes.

On the K menu (after you boot knoppix) there is an item called "Help" that has a user guide for KDE and a lot of other basic info, including the questions you posted.
Also, at the top of this page is a link to the "Docs" area of the site. Many will be too technical for you now, but after you exhaust the Help system you can look there for your more advanced questions.