@David9190
It sounds like you have been given a lot of misinformation.
@Gillian166 Is correct that the cleaning costs are set by the hosts. Some have cleaning fees, some don't and those that do decide the amount. Airbnb sets the guest fee, i.e. their commission. These costs should have been broken down on your booking, so they are easy to see.
I can understand why the host refused to cancel for your mistake. There are penalties, financial and otherwise, for hosts who cancel stays, so no host should do this lightly.
However, if the dates you actually wanted were available, which I assume they were as the host told you to rebook, there was no need to cancel anything. The host (or you) could have put in an alternation request to change the booking by one day. The Airbnb system would then automatically update the cost of the stay (and it should apply a discount if one is applicable, although it can sometimes be glitchy with that) and the other party just has to accept. It's a really simple process.
It sounds like the host didn't really have much experience of these things. But, when you 'called her out on her lies', I imagine that's what offended her and made her cancel your stay. Perhaps she was lying (no idea what she meant by Airbnb's cleaning fees or why she was trying to get you to accept a credit) but it might also just have been that she didn't know what she was talking about.
Likewise, the Airbnb rep misinformed you. All users, hosts and guests, have the opportunity to leave a response to a review. I would not worry too much about it though, because that response appears on her profile, not yours and, seeing as she didn't leave a review for you, no one looking at your profile will even know it's there.
@Gillian166 it sounds like the host cancelled on the day of the stay. I think in that case, it is possible to leave a review.