Why is my screen acting weird Black is turning green - but not everywhere and not on screendump or on my ext. screen (photo taken with iPhone). If I press the unibody hard on the left side, then I can make the green disappear, but that's not a solution.  

This is a MacBook Pro (15”, mid-2010) 2.66GHz Intel Core i7 with 8GB 1067 MHz DDR3, an NVIDIA GeForce GT 330M 512 MB / Intel HD Graphics 288 Mb, and the OS is El Capitan v.10.11.6  

To determine if the problem is caused by a graphics card or not, I would like to know if there is a way to have only one card/processor active at time?
If Cmd+Shift+3 does not capture the display as you see it, or, if mirroring the display on your external monitor does not reproduce it then it is not the OS which is making that happen.  

Your problem may be in the connection of the graphics and screen hardware itself. If pressing the unibody relieves this, you may need to reseat the graphics card or some other component. Has you laptop been dropped recently?

This Mid-2010 MacBook Pro teardown article or this disassembly video might help you ascertain which components you are pressing on.

Also, you may simply be overheating from a clogged vent port. Have they ever been cleaned (since mid-2010 = 6+ years)? This is a step by step guide to replace the fan if it needs a new one.