Re refund or any other transactions for that matter, it always has to be done via the Airbnb platform; any transactions carried out off/ outside the platform would be in breach of Airbnb rules.
Re refund for a day it's you choice to refund or stick with your chosen policy; you applied your cancellation policy which is clear in your listing so that's fair. It is the guest's responsibility to read the full listing details and if they are out of pocket as a result of not reading your description and making changes then you should not feel guilty because they are not happy - look at it this way, the guest is not happy because they can't get a refund but you won’t be happy if you give a refund, someone's got to be unhappy and it's their changes that have created this situation so they bear the cost.
Re cleaning fee, you are entitled to charge the cleaning fee because it is listed in your description. However, on this occasion I personally do feel you should refund full cleaning fee since you have admitted not cleaning the room. You could ask for a small amount to cover cleaning the new towels but to be honest, being that it would only be a small fraction, it's not worth the negative vibes - just my thoughts.
All the best however you decide to proceed,
Ama