With "mv," you can change the name of a file or move it to another directory--or both. Typing "mv cats dogs" will rename the file "cats" to "dogs," for example, while typing "mv cats ~/desktop" will move the file "cats" to the desktop directory without renaming it.
The "more" command allows you to see the contents of a file one screen at a time.
When you want to stop an application, there's no more efficient way to do it. Typically "kill" is used after "ps," which lets you find out the process ID of what you want to kill.
Part of the reason Linux is so secure is that only the root user has the privileges needed to install or remove applications and make other big changes. To install an application as a regular user, the sudo command can give you those root privileges temporarily. You will, however, have to enter your password.
Need to change your password? Then just type this command at the prompt, and it will ask you to type the current password and then a new one.
Keep in mind that the documentation that goes with the Linux distribution you're using can probably help. In Ubuntu, for example, the help section on the command line is a nice place to learn about the various commands and what you can do with them.
Linux.org's "Getting Started with Linux" tutorial is also a great place to explore.