If the query took minutes then either the datamodel has problems, they're trying to return far too many rows to reasonably display on a web page, they're missing indexes, they forgot to ANALYZE their database etc etc.
I think the answer is probably yes,yes,yes and yes. 😊
Truth is I don't have access to it at the moment to see whats going on but I suspect its badly written, returns too much and from what I understand maintenance is 0 so ANALYZE is probably a foreign word.