To respond to your question about the I, IV V notes or chords
1. Do not confuse the tuning of the instrument with the relationship of a string and a subsequent string. Since you are a Ukulele player, I will explain this in relationship to the ukulele
The tuning of the instrument is
The letter of the notes change as you go up the neck from open to 12 and beyond
If you look at your circle C is the 4th of G
Likewise A is the 4th of E
E however, if the 3rd note of the C major scale
If the open 1st string is the 4th of the open 2nd string, then that relationship holds true as you fret the second and 1st string on the same fret.
if, however, you started a scale on the third string open than the second string open is not the 4th scale note (in relation to the first note played but it is the 3rd note of the scale.
The reason we use I, IV, V is that those are the three basic major or minor chords we use to play a song and by fining the I, IV and V notes, you are playing the root notes of those chords.
Hope this helps.