Does it always have to be a plural form when you're saying "make amends"?
Yes it does. There is no phrase "make amend". The only option would be "to amend" which, as a verb means "to improve". To "make amends" means to repair a relationship or to atone for wrongdoing. Since they are talking about a bad relationship make amends is correct. Ex: He tried to make amends by apologizing. Ex: I'd like to make amends for my behaviour last night.