[susan53]

"to interview" can be used for any question/answer conversation - eg a job interview; a TV news interview with a politician, an actor, someone involved in a news event; police questioning a witness or a suspect; etc. It could be quite friendly or not, depending on the situation.

"to question" on the other hand suggests a critical stance. Some examples :
...when a reporter once QUESTIONED Lincoln in cryptic fashion, Lincoln refused to make any further statement.
...Pohl confessed the arson while being QUESTIONED about several fires in the Westphalia area.
...Government attorneys, Leavitt said, have QUESTIONED him closely about "five or six loans".

It's not relevant here, but "to question" also has the second meaning of "expressed doubts about" reinforcing the "critical" connotation.
...Lewis and Maund (1979) have QUESTIONED the true significance of social class,
...The governor was not used to having his integrity QUESTIONED.
...(The new passport) is essentially a travel document whose validity has been QUESTIONED by a number of countries.

"to interrogate" suggests that the questioning was "stronger" - possibly that it went on for longer, the questions were harsher etc. Example:
...Kenneth Starr and his deputies INTERROGATED Hillary Clinton for several hours at the White House [/b][/b]

"to interrogate" would also be chosen in a situation where threats, physical violence or torture were involved. Examples :
...The regime has INTERROGATED and imprisoned hundreds of dissidents.
...In the room there was no bed or mattress; nothing. Every day we were INTERROGATED and beaten.

All examples from https://lextutor.ca/conc/eng/