Can the word "program" be used to refer to the whole package of courses, facilities, people, funds, etc., in a certain discipline at a certain place?

This is an appropriate use of the word. The word program is quite general, meaning simply "a set of related measures or activities with a particular long-term aim". In this context, it could refer to any or all of the aspects mentioned in the question, but wouldn't necessarily refer to any one specifically without more context. A university that has an excellent mathematics program would be understood to have a high-quality course of study overall. That could include the instructors, the facilities, the curriculum, the funding, the alumni network, the job placement rate, or any other measure of quality.