Can I install Kontakt Player 7 and keep the full version of 6.5 installed for my DAW
Yes , that ought to be possible though what sometimes happens is that people and/or apps gets confused and opens stuff in the wrong version. And mind you , you can only open licensed libraries in the Player version.
Third-Party KONTAKT Libraries - Licensed vs. Unlicensed
My Kontakt Player Instrument Unexpectedly Switches to Demo Mode