The ability of columns to sustain a loading depends on their lateral restraint. The application of a gradually increasing load will eventually result in the column bowing (try it with a ruler on end). As it bows, the tensile and compressive forces increase and, eventually, the column fails.
The WTC external columns were restrained by floor trusses in one direction and perimeter beams in the other. The trusses - very lightweight structures with thin individual members - buckled from the heat from the aircraft fires. Eventually the joints failed, the trusses dropped onto the floor below, the column unrestrained heights became far greater and their load-bearing capability reduced. The great weight of the numerous floors above caused the lower unrestrained sections of column to buckle and fail and the increased load on the floors below, both from static and dynamic loads, caused these to fail in turn and progressive collapse to take place. It then gained an unstoppable momentum.
The splay on the lower sections of columns is nothing more than a failure plane from the progressive collapse. Demolition works make use of the knowledge of failure planes, that's why they would be the same.
With regard to WTC7, it started to collapse in the middle. If you look at the floor plans, there was a large span transfer structure here, so that is the obvious place where the steel will first buckle and yield from heat and, insodoing, pull the perimeters in.
Bear in mind that these buildings were designed in the 1960s to differing standards and they did not cater for progressive collapse. We only design for that now - and only for greater than five storeys - as a result of the Ronan Point disaster in 1972. But we still have thousands of high rise buildings where a similar collapse to the WTC could quite easily take place.
The WTC were designed for plane impacts. But the planes then were much smaller than they are now. And, no one considered the reality of avgas fires and the force of an explosion removing the somewhat poor fire protection to the structure. They would and do now, of course, plus technology moves on and materials and methods are available now that were not back then.
Finally, steel does not need to "catch fire" to fail. The temperature at which steel begins to yield and lose its elasticity is quite low. Even a domestic level fire can result in distortion to steels, so a fully-laden plane impacting it at 400mph would not have too much trouble there.
It's a testament to the design that the things managed to stand at all, for any length of time.
The conspiracy theories can be shot down in flames - ooh, that was not perhaps the best metaphor to use - by anyone with a modicum of structural training and a less cynical mindset from that which says that every bad thing in the world is ultimately due to American oppression.
'
