The main way of getting something known to staff is through a report, which requires evidence. If you don't have any evidence, nothing can be done. To also answer how things "shouldn't be a players problem" - I agree they shouldn't be but I don't think they are. Staff have lives outside of this, so should you, and have things to do outside of this server. Someone using the excuse that they are playing on a family computer is a funny one to not be able to make screenshots, as you could make these screenshots, send them into the report, then delete the screenshot off of your computer. It's so weird to see that as a valid reason to not have evidence, but the fact that staff have lives outside of the server and therefor there are times no staff member is online, is an "excuse" that is invalid to you. Interesting.
If no staff member is on, that isn't anybody's problem as the way to get a problem handled is to either tell an online staff member who will often times look into it immediately, or as fast as they can, OR to make a report with evidence. The fact staff logged off right before those messages were sent for your third example is nobody's problem, the players could just have made a report or dmed one of the staff members on discord to ask their question. I don't see problems with the things you have mentioned; It's a simple case of the fact staff are volunteers, they have lives outside of the server and don't see every single message. If you think a Helper rank will fix that, I suggest making a suggestion for specifically that - backing up why that needs to be added with concrete evidence, not just words.