4 Along with TrevorD, I'm in the UK. I've seen w/o for without and w/ for with, but not b/c. They are not suitable for formal use. It's potentially of interest that the Pitman shorthand symbol for w resembles w/ and is often used on its own to mean with.
Normally one would just say without problem, skipping the any altogether. It doesn’t really add anything to speak of, and just makes the phrase longer. But I certainly wouldn’t call without any problems (or with no problems) ‘wrong’. Also, you can swap in trouble for problem in all those phrases, and you get the same answer; think also of no trouble found.
I was watching a speech on TV by someone who said the sentence "..and our country faces threats from within [long pause] and without." I thought this was wrong and jokingly posted about on social ...
Your friends are people you know well and like spending time with. You can refer to a friend who you know very well as a good friend or a close friend. He's a good friend of mine. A close friend told me about it. If someone has been your friend for a long time, you can refer to them as an old friend. He or she is not necessarily an old person.
Definition of a friend: One who walks in—when the rest of the world walks out. John and I have been friends ever since we were roommates at college. Trust is important between friends. I used to find it hard to make friends when I was shy. We became friends in the war and remain friends to this day.