It's actually nothing like that, because the toilet paper is the ear training, and if you're done the ear training you shouldn't have a problem.
Here's the simple answer to your OP:
"I don't know what scale to use over what chord in what key etc..."
Use the scale of the key, unless you have non-diatonic chords. If you're learning your theory this should become obvious really fast. Keys are either major or minor, and are loosely based on the major/minor scale. If you understand the notes in the scales, and the resulting chords generated by that scale then you should know which chord are diatonic and which or not. This is n't an issue of "ear training" in the formal sense, it's just an issue of understanding underlying harmonies when you're soloing and developing a repertoire of things to play over them.
If you need more clarification on the above, LMK. If you understand the above then begin practicing 2 octave arpeggios over each chord in a progression you're trying to solo over, transcribe lines (if you can find them) of other players playing over similar progressions. The idea is to hear the chord change and understand how to treat it, the scale of the key is the foundation of the notes you'll choose from, and arpeggios of the chord are more specific, inside ways to treat each chord.