Now that I have uploaded a video on modes, I expect a few dozen questions to be posted here. The first question I got was what chords work over each mode. Well - The parent key has 7 diatonic chords to it. Does anyone KNOW what those are first?
The modes are grouped into major and minor modes - its all clearly stated in the video. Major means all the Major type chords will work such as Major, Major 6, Major7, Major 9 with the exepttion of the Mixolydian mode which has a flat 7 so you cant use a natural 7 in the chord so that Major 7 and Major 9 must become 7 and 9 dominant chords. Minor - you just look at the scale - Dorian has 1 2 b3 4 5 6 b7 and 1 so the chords based on the root would be of course: 1 b3 5, 1b3 5 b7, 1 b3 5 6, etc. Look at the other minor modes and figure out what you have to do to the chord to make it fit.

Believe me you can play out of key (this is what you mean by out of "tune" I am sure). Its not just running chromatic scales and playing random chromatic notes. You have to ingest the modes and the chromatic notes into your subconscious by internalizing them in your practicing. You have to sing them as you practice them against backing chord tracks to make yourself aware of each tone and its gravity. What you are suggesting is like kids playing randomly in a sandbox. What I am suggesting is MEMORIZING the EXACT sound of each note against different chord qualities. You need to learn how to listen critically not just riff around on the neck.