Unlike a dog, cats can stay indoors all the time. They don't need to be walked like dogs do.
Some cats, however, are outdoor cats and thusly, they do their own thing (go to the bathroom, hunt, eat, etc...). It's up to the owner whether they choose to have their cat an indoors or outdoors cat.
About the leash, I can't help you on that one. Since our cat is an indoors cat, we have no need for a leash. I have heard stories about leashes and how complicated they are to use.
Sorry if i've been no help.