What does (don't slouch) and (don't be slouchy) mean? And where is their usage?
In the literal sense, to slouch is to not stand up straight. If you have poor posture and your shoulders are sort of rounded forward, you are slouching. Mothers will often tell their children "don't slouch!" because they're afraid they'll grow up with a crooked spine or some such maternal worry.
In a slang sense, to be a slouch means you're not doing your best, or doing just enough to get by and letting everyone else carry the load. It's often used in a sort of 'opposite' type of statement, meaning the person has a special skill or talent: "I don't like to brag, but when it comes to cooking, my mom's no slouch."