No one actually fully answered the original question yet.
Is there a tool I can use to see my screen on the mac, control it, etc?
You can control your idevice (not only view it's screen) given you have a mac / PC paired with it (that is, you had them connected in the past using USB cable, and pressed the "Trust" button on the iPhone's screen alert).
There are a few UI automation tools that are capable of doing that. Try the evaluation version of SeeTest Automation for instance.
You will be required to generate Apple's provision profile unique for your iPhone (in an automatic, free of charge process) which will allow viewing and controlling your phone, managing applications etc.
EDIT (or How To Trust a Device with Broken Screen)
What you will need:
- Having Siri turned on / triple tap on home to activate VoiceOver
- a bluetooth keyboard.
Lightning to USB adapter.
- a simple USB keyboard.
If your device was not previously trusted by any computer, and you cannot tap "Trust this computer" on your broken screen, you might be able to use VoiceOver with a USB and Bluetooth keyboards to virtually tap trust (and generally to control the device) even with broken screen.
The trick is to bring up the trust alert by connecting the lightning port to a computer running iTunes (or Xcode), and then tap the "Trust" button using
Space / Enter key on VoiceOver and a bluetooth keyboard (this must be a bluetooth keyboard since the USB connection cannot be used for communicating with the computer AND with a keyboard simultaneously).
If you have a bluetooth keyboard paired with your Apple device,
great. Just connect the device to your computer, open iTunes and hit Space (not sure right now, maybe it was Enter...). If you have problems with that, or you are not sure whether the alert is displayed, read further and turn on VoiceOver.
Turn on VoiceOver:
- To do that, use Siri (assuming it is configured). Just Say "Hi Siri,
turn on VoiceOver".
- If Siri is off, some iOS versions are configured by default to turn VoiceOver on/off using triple tap on home button.
- If you have a paired bluetooth keyboard, skip to step 6. Now that VoiceOver is turned on, you will need a USB keyboard to navigate to the Bluetooth settings (of course, if the screen still responds to touch you will not need the keyboard, just listen to the instructions and tap):
- Connect a USB keyboard to the device using Lightning to USB adapter (it is meant for camera, but will also work with standard keyboards).
- Navigate to the Settings app using VoiceOver (this is a tricky part, controlling VoiceOver is a mastery...). Basically the Left / Right arrow keys are used for navigation of UI items, Left + Right keys for "Quick Nav On" and Up + Down keys to activate an item.
- In the Settings app, go to Bluetooth settings and pair the keyboard.
- Once you have a bluetooth keyboard paired, connect the device to a computer, and control VoiceOver with the keyboard to trust it. Now you can proceed to using any viewing tool you like.
P.S. You might also be able to see your screen without trusting the device (and using Quicktime) by using a Lightning AV Adapter. But I've never given it a try...