Hi Helena: as a native Mandarin speaker I would say the sentences you presented were not easy to translate as there are a lot of dedicate references in some words such as "哥们儿" “好意思”. I tried by best to give you the directly meaning, but I guess you would need more context to precisely grab hold of their meaning.
1. but sometimes it was the bro (brother, which means 哥们儿) who caused the problem.
2. when do I deliver it for you tomorrow, bro?
3. this is one was a bit hard to translate directly. It was a very indirect way of saying "I don't wanna causing any inconvenience" but it also has the meaning of "If you would deliver it for me, I would appreciate your help."
4. Directly translation: There is no shadow of that bro; indirect translation but with more precise meaning: I can't find that bro anywhere.
5. I was thinking of your issue all day long but unfortunately the guy whom I need is not here today.
6. Look at the thing I did.
7.Alright, please don't worry about it, I have another bro. (You might know that the character "还" can be translated in "also, as well" in English, but in this case, it doesn't mean"I also have a bro" but means"I have another bro which can help", according to the context you gave me)
8.what else do you say, bro is bro, you don't want to be critical/strict/mean, right?
both "哥们儿" and “兄弟” refer to either 1. your biological brothers, or 2. somebody who is a close friend to you, so they can be used interchangeably.
"计较"basically refers to caring about some tiny things too much (such as money, benefit, etc), of course, in a negative way.
I would say these sentences are often used by boys/men in China, especially oral Mandarin, but it 's not easy to fully understand for the beginning learners. Hope my answer helps!