If a volume control in my app changes value, should it globally change the system volume or just for my application?
Out of experience, in the earlier versions of Windows Phone, the volume was global. So if you lowered the volume for ringtones and notifications, it'd also get lowered for everything else. That was annoying in cases where I wanted to play music on my headphones for example, increase the volume and later the phone would blast ringing.
If sounds are an imperative part of your app I think you should let the user control it specifically for your app.
For a Windows PC:
You have something called an Audio mixer that does a decent job of synchronizing the volume of all running application with a sound output. It maintains the volume levels, scales and suppresses sound based on your master volume control (i.e. speaker output)
So by default increasing the volume of your app should only focus on increasing its sound output and it should not control the system's volume - unless you provide an explicit option to do so.
Image showing volume synchronization at a PC/Speaker level over multiple apps. Notice how the mids for the individual sounds vary based on the master control