Living things can use ATP like a battery. The ATP can power needed reactions by losing one of its phosphorous groups to form ADP, but you can use food energy in the mitochondria to convert the ADP back to ATP so that the energy is again available to do needed work. In plants, sunlight energy can be used to convert the less active compound back to the highly energetic form. For animals, you use the energy from your high energy storage molecules to do what you need to do to keep yourself alive, and then you "recharge" them to put them back in the high energy state.
However, proteases do not catalyze the hydrolysis of all kinds of proteins. Their action is stereo-selective: Only proteins with a certain tertiary structure will be targeted. The reason is that some kind of orienting force is needed to place the amide group in the proper position for catalysis. The necessary contacts between an enzyme and its substrates (proteins) are created because the enzyme folds in such a way as to form a crevice into which the substrate fits; the crevice also contains the catalytic groups. Therefore, proteins that do not fit into the crevice will not be hydrolyzed. This specificity preserves the integrity of other proteins such as hormones, and therefore the biological system continues to function normally.