Nope, and nope.
Once you learn your instrument, I've been playing for 17 years but really REALLY hunkered down on the theory aspect for the last two, you will be able to know these things in your head.
You want to be able to visualize the fretboard in your sleep. This comes, not from luck or just being a natural (though that helps too!), but from three things; practice, determination and experimentation.
Learn your major scale, on the guitar it's easy to do in all twelve keys, because once you learn it in one position, then it's the same in all other 11. Learn the names of the notes and where they are located on the fretboard. Then, learn their relation to the chord your playing.
For instance, the cycle of fifths (or fourths if you go the opposite direction), is a great tool for many reasons. Take a simple melody like "All The Things You Are" written by Jerome Kern. There the thrid bar of the head I think, over the Eb7 chord, where the melody note is four quarter notes of G. So, you can now go around the circle of fifths, using the melody note. G is the fifth of C7, the root of G7, 4th of D7 and dom7 of A7. This will help you learn the relations to the chords. Also, try using the same method chromatically....G is the fifth of C7, #5 of B7, 13th/6th of Bb7, and dom7 of A.
All this will eventually open new doors. I never understood what that meant, exactly, till a year or so ago. When you start actually APPLYING these things, then your ears just start hearing them and you suddenly start doing different things in the same songs you've been playing. In other words, new doors open up.
