Go to System Settings/Display, and look for an option for Sleep. You can adjust how long the tablet will remain idle before turning the screen off.
Apps are best installed from a legitimate app store like Google Play or Amazon Appstore. Not all Android devices are approved for Google Play--since you have an off-brand device, it might not be available to you. It's also not available in every country--where do you live?
Your device probably came with a link to some kind of app store--look for a shortcut to something that sounds like a Market. You could probably also install Amazon Appstore by opening your device's browser and going to
www.amazon.com/amazonappstoreapp, and following directions from there. Before you install, make sure you go to System Settings/Security, and check the "Unknown Sources" box (if there is one), which allows installation of apps outside of the official Google Play Store.