This is your general run of the mill acyl substitution reaction. Acid chlorides are the most reactive carboxylic acid derivative, so this reaction should be quite speedy.
To answer your second question, the truth is that acyl substitution is occurring at both hydroxyl groups, however it extremely favors the one indicated in the photo you uploaded. This is due to steric hindrance (phenyl groups are bulky, and it would be difficult for the acid chloride to meander its way between two of them). Only one substitution occurs because the acid chloride is so reactive that all of it will react with the reactant at the most available position possible. (There is not one of the reactant molecules present. Rather there are many)
