If I rent a place for a period, and then I want to stay longer (with host’s approval) and I extend my stay (do not make a new reservation), do I pay the cleaning fees again?
That depends on the host. I reverse the cleaning fee when guests extend their reservation. As you indicated in your other post that you are looking for a long term stay; your host might insist on cleaning periodically.
We extended our stay in Rapallo, Italy, with the host’s prior approval. He didn’t wave the cleaning fee and I was fine with that. Being a host, I know that sometimes, longer term guests means more cleaning after they leave. If my guests are there for 2-3 days, it’s usually a snap to clean. Ten day guests usually adds a couple more hours and sometimes double the hours it takes to clean my place.