Order of technician calculation with accumulative power moves

The Power of an attack directly correlates to how much damage you deal, because its presence in the damage formula is entirely multiplicative. So, an attack with 120 power will do twice as much damage as one that has 60 power. The same goes with your corresponding attack stat: a Pokemon with 100 Attack will do twice as much damage as one with 50 Attack when using the same attack on the same target.

STAB has operated consistently since Gen 1 so this applies to all of the games. It increases the Power of an attack by 50% if it matches one of your types. 60 becomes 90, for instance.

Technician increases the Base Power of an attack by 50% if its Power is 60 or less. So the most you get is boosting an attack at 60 power to 90. This occurs before STAB is calculated, so your Power would be 90 for STAB, boosting it to 135.

1) What are the exact conditions for additional Boxes to appear and do you always get 8 additional Boxes? (Using Pokemon Bank reveals that in X/Y, the maximum number of Boxes is 31, which I have experienced to be unlocked in 2 steps of 8 Boxes each.)

More boxes appear when you have at least one Pokemon in your current boxes. When all your current boxes have at least one Pokemon in them, 8 new boxes will appear the next time you log into your PC (you start with 7 boxes, then get up to 15 boxes, then up to 23 boxes and last to 31 boxes, the figures exclude the battle box).

2) Do additional Boxes you receive stay forever or do they disappear if the conditions for them are no longer met?

3) If they disappear, is there a way (such as renaming or putting any Pokemon in the last Box) to make them stay no matter what, even if you released all your other Pokemon?

No matter what you do, those boxes will never disappear, even if you move all the Pokemon you have to a single box and the remaining boxes are empty.