use phones usb for directly controlling and powering something
I want to control the power.
  
  1.a) Is there a way (Writing app or ...) to get my phone to output usb pwm?


No.


  1.b) I dont necessarily need the fast rate of pwm. So is there any way (Writing app or ....) to turn on and off the power of the usb output?


Highly unlikely.


  Can I read incoming data while powering and can they be outside of the usb protocol? This is supposed to mean: Once my Phone has done its work I want to give a signal onto the D- and/or D+ of the usb cable to tell the phone that it should stop giving power. That signal will not be in the usb protocol but will rather just be some voltage. For that I would need to be able to directly read the usb income and control my phone based on that. Is that possible? In Short: When I want to be done powering I put a Voltage of e.g. 3.3V onto D-/D+ and the phone notices this and turns of the power. So the questions are:


No.


  2.a) can I power something and read data over the same usb at the same time?


Not in the way you talk about, no.


  2.b) can I directly read the D-and D+ pins and use them to control my program?


No.

USB is USB. You cannot use it for anything except USB. 

You set the type of device (HOST or DEVICE) by setting the USBID pin (pin 4) of the USB socket to the right voltage (GND or 5V [I forget which is which off hand]). The phone then either enables or disables power from the VBUS pin (pin 1).

Any signalling is then performed using LVDS on the D+ and D- pair conforming to the USB protocol specification.

The only exception to this is when the phone is connected to a charge-only port where the static state of the voltages on D+ and D- indicate the current the charger can provide. This is done (usually) in hardware.

If you want to do anything at all through the USB other than just sucking power out of your phone you will need to add an active element that speaks USB. That could be a microcontroller, or it could be a discrete USB chip, such as an FT232 or similar device (there's many different options on what IO protocols and facilities are provided on the different chips - from UART through SPI/I2C, to parallel).