That's called a trackball. The device stays in place and you move the ball (usually) with your thumb, rather than moving a mouse which in turn moves the ball inside (or with the newer optical mouse, electronically senses the mouse motion).
A place where orphans live is called an orphanage.
The people who live in a particular place are called residents or inhabitants.
It is called a clicker If you mean the built in mouse, it is called a touch pad or mouse pad.
It is called an "Asylum"
A baby mouse is called a pup or a pinkie.
A female mouse is called a doe. (and a male mouse is called buck) newborns are pinkies
There are many species of mice. Some that live in meadows and fields are called field mice. The term is not scientifically precise.
If she doesn't come when called, set a live trap. Make sure you set it in a place she is likely to visit. You can do this, but it's unlikely you'll get her back.
Mickey mouse lives in my TV.
In Christianity, the place where angels are believed to live is called Heaven.
at a place called kirawaya