The grain is caused by the camera using high ISO...
Basically for the camera to calculate the exposure, the light bounces off the subject and into the lens.
Because the camera is exposing for the cat, there is not enough light, which is why the patio door is washed out and there is a lot of grain introduced. Try using the Av mode more. The lower the number, the larger the iris, thus more light gets in, and the larger the number, the less light gets in. Just play around with that for the time being and note how it affects your shot.
Hope that helps.
Here's my contribution. I fucked up on the unmasking and edges, but I got lazy =)