In Mandrake, to change the screen resolution,go to the Mandrake Control Center by clicking;
start-->system-->configure-->configure your computer-->
You will be prompted for your root password. Type it in and hit "OK"
Click on the hardware menu on the left...then "screen resolution.
You can also get there by clicking the icon on the panel on the bottom. Run your mouse pointer over the icon monitor with the wrench next to it. you will see "configure your computer" pop up. So you can click on this to get to the control panel as well.
Just be a little careful and make sure that your monitor and video card can support what resolution and bits that you want to choose.
It sounds like Mandrake is shutting down properly, but just not powering off the computer, correct? This is a function of Mandrake interfacing with the computer's bios correctly. Depending on your system and what you enabled (or disabled) for power management during the installation (and the bootloader) this can happen. You can just push the power button to turn off the system completely, or try to make a change or two to the bootloader to enable or disable power management.
What computer system do you have (model and make)?