Several types. Biofeedback aims to decrease the body's stress response by making it conscious & thus more controllable. Examples: pulse monitor (high heart rate), skin temperature (stress lowers blood flow = cooler), and gsr (subtle sweating measured by electrical conductance, more w stress). Any of these approaches can be effective with practice. I don't know about specific (smartphone?) apps though.
Why? Don't use devices to "monitor" stress. Find tools to treat, manage, and especially to limit/prevent stress.
Quite a few. Agree; better to evaluate/treat. There are a number of apps that can be useful for tamping down the stress response. You might check out those that have been reviewed by HealthTap docs. One good free app is, "Breathe to Relax." One that you have to purchase that is a bit on the pricey side is Emwave by HeartMath that teaches you how to decrease heart rate variability. Hope this helps.