Can jinn take the form of a fly in the house, and if someone swats it, unaware it is jinn, and then experiences possession, what should they do? And can one be possessed in the mosque while supplicating, or are jinn unable to enter the mosque?

It is not possible to definitively confirm or deny whether jinn can take the form of flies. Jinn can assume various shapes, including those of animals such as snakes, dogs, and black cats, as well as human forms. Shaytan (Satan) may even enter a mosque to harm people. If someone is afflicted by a jinn's transformation, the lawful Islamic ruqyah (exorcism/spiritual healing) is their cure.