1. I think you can resize partitions in Mandrake Control Center. I don't know if you can resize your root partition using Mandrake Control Center since your OS would be running off of it while using Control Center.
2. Linux is USB compatable. If you have a Linux driver for your DSL Modem, then it should be able to work.
3. There are two different formats commonly used for installing programs. RPMs are the easiest to install. All you need to do is double click them. Just make sure the RPM package you are trying to install was designed for Mandrake. The other format and the most widely used are compressed files in the .tar.gz format. To install you first have to start Konsole, type "su" and enter your root password to set Konsole in root user mode, decompress the .tar.gz file (usually "tar xfvz ***.tar.gz"), "cd' into the folder that was decompressed from the .tar.gz file, and follow the installation intructions found in a README file or something similar. Open source programs tend to be distributed as just source code you compile yourself. Usually the you compile them by "./configure" then "make" then "make install". Closed source programs tend to be distributed in an installer that you execute by typing a command like "./install-***".
*note: where I have placed "***", what you type depends on what you are installing.