Why can light waves pass through other light waves without interruption?
because of they are particles.
Because the are not completely dependent on matter like other wave types.
A particle has a specific position and a specific size, so they cannot pass through other particles. The properties of a wave are very different from the properties of particles. Waves have a specific frequency. Waves have no specific position and specific size, so they can pass through other waves with no trouble at all.
They can't. Read up on destructive and constructive interference. When waves are in sync, they build each other up...that's called constructive interference. When they are 180 degrees out of sync, the cancel each other out...that's called destructive interference. The so-called two-slit experiment demonstrates both kinds of interference. Essentially two slits are put in a barrier and a single light source is shone through the two slits. The light passes on to a screen where alternating bright and dark bands appear. The bright bands appear where there is constructive interference and the dark bands appear where...you guessed it. The reason you don't see these bands without the slits is because, the light and dark bands over lapped. That is, the light bands fill in the dark bands; so we can't see them when there are no slits.