I suspect she is trying to catch a bird. The other day when we first spotted her, she was lying in the shade directly under the bird bath.
As to the he/she determination, could any critter with a face as sweet as this be a guy? I think not.
I had just read that a cat with rings around its tail is a trait tracing back to its feral ancestors. This cat is beautifully marked all over.
But she will NOT become part of our family. Enough is enough.
However, she is welcome to the back yard.