@Sam5278
1. There are very good reasons why a host insists that you communicate via the Airbnb messaging system, especially about any issues. Basically, you need to have a record on the messaging system if anything goes wrong, e.g. a guest trying to scam you for a free stay. This is normal.
2. Perhaps the host was slow in responding, but if you were using the App, it is glitchy and messages often get delayed, not just by 20-30 minutes, but often for hours and, occasionally, even for days.
3. I have no idea what location your airbnb was in, but I do know that where I am it's virtually impossible to get a plumber out the same day, especially if there are parts to be bought, and the following day would even be a small miracle. So, quite likely the host was doing everything she could to get the part and someone out to fix the problem.
4. Maintenance people show up late all the time. Sometimes days late. A delay from 10am to 11.15am is nothing. That is usually out of the host's control, but she did let you know.
5. The host should have let you know when the problem was fixed, but perhaps she could not get an answer from the maintenance man (takes me sometimes days or weeks to get responses from tradespeople, that's just normal) so perhaps she was chasing for an answer on this. Ideally, a host would either be nearby or have a co-host nearby to go and check on the situation.
6. Not sure why you were expecting a late check out because of this? Did you ask for one or were expecting the host just to offer, somehow being psychic and knowing that was something you expected? If the host had other guests checking in on the same day, this could well have been an impossibility, which is why it was not offered.
7. Yes, I do feel that you deserve some compensation for this. Not having a working shower is not okay. So, message the host and ask for one. If she refuses, you can raise a claim with Airbnb but, in theory, you are supposed to do this within 72 hours of noticing the problem.