A plucked guitar string or any string for that matter will vibrate at some given frequencies. These frequencies will depend on the length of the string, the density, and the tension. The string is held in place at the ends by the instrument, so here the amplitude is zero. All waves that end up having zero amplitude at the fixed ends are valid harmonics. See picture from Wikipedia below:
The first harmonic is normally the loudest one, which we would tend to identify as the tone/note played. Then we have the next harmonic with double frequency, the third with three times the frequency, and so on. So the harmonics or overtones are integer multiple of the first tone.
The characteristics of the string will determine the strength of each harmonic, and the rate at which each harmonic will decay. The string tension, length, and thickness are probably the three most important factors, but the material type, and other things play a role too. The instrument body will also affect the strength of each harmonic and add some resonance. The harmonics are the reason you can hear a difference between a piano string, a guitar string, a bass string, and so on. They work on the same principles, but the combination of harmonics is what sets them apart.
On a guitar the same principles will determine how a note will sound depending on where on the fretboard it is played.
Voicing a chord with a note presented twice on different strings is no problem, if you think it gives the right feel and sounds good. That is probably a question of artistic freedom :)