In order to destroy other player’s buildings in your villages you need to attack the city from which the buildings were constructed with mission Buildings Destruction.
If the City Gate is closed, the city can’t be attacked, thus the buildings can’t be destroyed.
In course of the "Buildings Destruction" mission, the army Total Attack value matters to how many buildings will be destroyed or damaged.
If an attacker wins then at least 1 building will be destroyed or damaged.
Logic of damage calculation is as follows:
On the end of the battle (after round of resurrection) at least 200 points of Attack for each level meant to be damaged will have to remain. Whether the damage will happen or not, will be defined at random.
In other words, even if there’s enough Attack Points, the damage can be less than maximum possible.
If there’s enough Attack Points for all levels of all building destruction, then at least 1 level of each building will be destroyed; if not – some of the buildings can remain absolutely untouched and some can be partly damaged or fully destroyed.
If you have chosen the type of building for destruction that the defender has no, no buildings will be damaged at all.
Workers, Builders, Special Units, also Special Units on training, which are in buildings at the moment of damage or destruction – will die.