Hello, at first reading, I found the verb tenses a little confusing. so I made some changes. The corrections are in blue and green (for an alternative). The red wordings are problematic - you need another synonym of place and rest.
yours was interesting observations.
A fly is/was flying around my head, it had just came just through the window. Now it's leaving me alone towards a cutain hanging on the kitchen. A flower basket set/sits on the table and the fly throws itself at the basket. Let me see another place which it wants to sit. A garbage bin in the corner of the kitchen is a good condition to be taken up by a fly (??). To sit there, it goes around back/comes back over my head and told /tells me it is able to do everything it likes and my permission has not any role in this/its play/game. After ending the project, this little creature is going to leave the house through a wide open door.