Sometimes we get annoyed at an act someone’s done, or something they’ve said. If I was to speak to someone else about this regarding how it annoyed me, is that backbiting?

1- It depends on how you say it. If it’s said in a way that affects that person’s reputation and opens the way for them to be mocked or insulted, then it’s haram. If it’s said in a very professional and polite way, such that you don’t question the other person’s character, it would be ok.

2- If what the other person did was a violation of your rights, or that person deliberately wanted to annoy you, yes you can tell someone else about it since you would be oppressed in this situation—even if affects that person’s reputation.