Hello.
Thank you for your query at DoctorSpring.com.
I understand your concern.
As per your description and pictures, you seem to have anal warts, flesh like lesions at the Anal opening. These are caused by Human paillpma virus and can be transmitted sexually. They can be left alone if they are not causing excessive discomfort. If excessive discomfort is present, you can get them removed surgically.
In prolapse, some part or whole of the inner layer of the rectum and anal canal will come out which doesn't seem to be your case from the pictures. However, it has to be confirmed by a surgeon after clinical examination.
It is not advisable to have anal intercourse as it will only worsen the condition.
I request you to meet a general surgeon, confirm the diagnosis and proceed accordingly.
Feel free to ask queries.
Wish you good health.
Regards.