Some great replies have already been given, but I’m just going to go through all of them neatly.
友好 - Not particular sure why this one is problematic, sorry.
仲良く - Almost every time I hear this it’s used with suru to mean along the lines of “To Get Along.” If you watch anime, this phrase pops up all the time. For example, parents say it to their young children who refuse behave around other children 「仲良くしなさい」, and high schoolers (especially females) use it to try to loosen up a classmate who is giving a cold shoulder or picking a fight [仲良くしようよ」. It’s a “good relationship” as an adverb, hence “friendLY.”
親友 - Another one found in anime a lot as well as VNs. Take a quick look at most harem series and you’re bound to find the obligatory 元気 male friend who wants in on the harem attention and the typical line that follows when a popular girl says something cute to the MC or makes a cute expression: 「親友ですね？」. If I remember correctly, Matoi uses 親友 to the MC of Fate/Extra Last Encore in episode 1 to justify stabbing him.
人格 - As other replies have mentioned, this is “character” in the meaning of having a particular set of traits. “He’s a man of good character.” It describes how they are 「格」as a person 「人」.
性格 - This is a person’s natural disposition: it’s how they are 「格」 by nature 「性」. Unlike character, which is developed by how you are raised and the experiences you go through, this is your innate set of attributes that control how your character develops.
For example, the rich guys in a lot of stories (Japanese or otherwise), especially those in arranged marriages with main females, often exhibit very great character: they are polite, mannered, and patient gentlemen by whom every female wants to be courted. They have a good 人格. However, the inevitable plot reveals they are actually a scheming rat who only wants to inherit the influence of the girl’s family after her father dies. He has a terrible 性格. Ultimately, of course, this character is completely bad, but 人格 can only be determined by a persons statements and actions and thus can be faked much more easily. 性格 is your base personality, and faking it requires much more effort to not be seen through.
Hope that helps a bit!