Yes it is normal for cats to eat grass. They eat grass when they have an upset stomach, kind of like a human taking a rolaid. Usually they will throw up the grass afterwards so you might be prepared for that. It's normal, don't worry.
Pretty normal. Pretty safe. They may vomit afterwards because they are unable to digest grass, but it's nothing to be worried about. The old tale is that cats and dogs eat grass because they're sick. This is false. Cats and dogs eat grass because they're sick. They eat grass because they're moody. They eat grass because they're happy. They eat grass because they're healthy. And they even eat it because they love you. In other words, they eat grass for no other reason other than it tastes good as far as we can tell. :)
Yes because I heard that grass is a cats medicine
Yes. They may toss their cookies afterwards, but that's the intent.