Yes to "the" and it depends to "at". "in" would often be more usual : He works in the Fung King Hey Building.
"at" is usually used for a place which is both inside and outside, and when you're being vague about exactly where the person is - eg : He works at the station.
Does he work in the ticket office, or outside on the platform? Similarly at the hospital
, at the university
- all three places are large areas with both buildings (inside) and grounds or outside areas. But a building, by definition is generally "inside".
You might however say : I'll meet you at the Fung King Hey Building
, where you're not actually specifying if you want to meet inside or outside.
For other differences in the use of "at" and "in" with institutions, see here : in or at