waves
For what I knew, interference of two waves is their sum. The classical examples I had in minde were the two pulses, either same amlitude or one positive one negative moving in opposite directions. You get the result of their interference in time at each instant by adding them. So you get constructive interference when they are both positive and add up, and destructive when nothing is left because they perfectly cancel out.
But also the idea is that waves do not change themselves, they do not disappear. If after a while one of them takes a different path, it keeps all caracteristics as before meeting the other. Interference I believe affects the medium at their encounter spot.
But that's slightly outside the subject...
I'd say that waves interfere no matter what their pahse difference is. So your two waves interfere (add them and you get the interference result).
The thing is that the easiest way to imagine interference is seing trains of waves go one over the other and their addition result. I remember that the best exmaples to understand were visual: water waves or light waves... But water is still best.
Destructive and constructive interference are just special cases of interference, extreme results. That's why they get named all the time. When ripples coming from two sources , on water, collide, they have points of high and low ... theose are the extremes of constructive/destructive interference, if not in all the other points, they are still result of interference, the addition of the two waves, each of them 2 dimensional, for which is you had the equations in space and added the values in that point (x,y) in space you would get the resulting "amplitude".
The phase issue is: when two sinusoids are 180 apart, they are in opposition, so their sum is 0. But if it is the same sinusoid , same frequency. Same goes for 0 dephasing=> constructive. If they are 90 degrees apart... try a simulation.
Why after superimposing they continue safely and unchanged? because each wave has a direction, a frequency, dictated by its source. Sound waves alter the air's molecules' movement, but they hold on to their direction. If someone were to call you from behind a crowd talking loudly, it would mean that you would never hear your name. But you do. ( The fact that your ear has a special filter and a habit of hearing your name called is the second part, it's the reception...)
That means that the wave of sound carrying your name , even after colliding with the others, kept it's direction and strength (as much as air does not trouble it, because waves suffer from attenuation, etc because of their transmission mediums...)
I honestly do not know if mathematics proved it, it's beena few years now... But I think that if you write the equations of two waves thoroughly with all parameters (time and space normally) and add them, you can still se that the result is made of two, so even after time passes, you can see that the sum is made of two separate components, so if space directions differ after a while, they will continue unharmed
I'll try and get back with more solid stuff if I can