All very relevant answers above
The first detail: the phase of the moon is based on the relative positions of sun, planet, and moon. If the moon is between sun and planet, it's new. If the moon is on the far side of the planet from the sun, it's full. If it's off at a right angle, it's half. Basically, where the moon is in the sky, it's shape, and the current time will tell you where the sun is relative to the observer's longitude.
What this basically means is that if there are two moons at different positions in the sky, their phases must be different. It's simple geometry.
As to the other questions that fall out of this… It depends how distant your moons are from your planet, which direction they orbit (unless it's a very newly captured moon – new being measured in eons – it will be within a few degrees of an equatorial orbit), and other considerations. To make things messier, if the orbits are such that the full phase cycle of each is almost identical (see caveat), then their distances from the planet are very similar, and they are going to be attracted to each other when they get close, resulting either in a crash or one being flung out of orbit and the other likely being flung planetwards. (All very fun!)
The caveat is if they have the same cycle, in which case they are at each other's Lagrange points (L4, L5), so the same distance from the planet, 60° apart.
The secondary caveat is if the two moons are very different in size, it's possible for them to be in nearly-identical orbits, but when their paths cross, the smaller one "switches" position, moving its orbit inside or outside the larger moon's path. And, yes, this can be a stable system: there is a pair of asteroids in solar orbit that do this. (Whether it can reasonably happen with large-enough bodies to be considered planetary moons is less certain.)