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You could better say it like: "Are your exams finished?" or less common but still correct "Have your exams finished?" (because the way you are saying is called 'declarative questions', which would look odd here.)

You could also (more commonly) say it like this:"Are you done with your exams?"

All four are grammatically correct, as long as you don't specify when each event happened.

2. There has been a serious discussion at home.

Is grammatically correct.

Yesterday, there has been a serious discussion at home.

Isn't. Rather, you would write/say:

Yesterday, there was a serious discussion at home.

In all these cases, the present perfect is used to emphasize on the result. For example, take the sentence #3. You could use either the simple past or the present perfect.

There was an accident on the way to school.

Is a casual and descriptive way to say that an accident happened, simply.

There has been an accident on the way to school.

Is used to emphasize on the result of this accident. For example, it could be an excuse for you being late.