Could this three moons system be stable?
I see no reason why this wouldn't work.  The innermost Galilean moons are in a 1:2:4 resonance so it's clearly a stable orbital configuration.  They could all be tidally locked if you want, but the planet itself can't be tidally locked with all of them.  If the planet were tidally locked it would likely be locked with the innermost moon.  

Also of note, the Galilean moons all have eccentricity less than 0.01 and inclinations less than 0.5 degrees.