Is delaying beyond a pre-arranged work appointment without an excuse considered breaking a promise, and is not corresponding with a non-Muslim professor and not going out for coffee with him considered breaking a promise if no specific appointment was set?

The first scenario in the question involves breaking a promise, and the second scenario is likewise [problematic] if there was an intention from the outset not to fulfill it. Fulfilling a promise is considered mustahabb (recommended) by the majority of scholars. Allah has commanded it, and the Prophet (peace be upon him) warned against breaking promises, considering it one of the characteristics of hypocrites. Some scholars view fulfilling a promise as wajib (obligatory) and that one who does not fulfill it commits a sin, especially if there is no valid excuse. Breaking a promise is even more reprehensible if it stemmed from an initial intention not to fulfill it. It is recommended to fulfill a promise even to a disbeliever and when inviting a disbeliever to Islam.