Meaning: become very angry, act crazy.

Example:
She’ll go bananas if she sees the house in this (dirty) condition.

Meaning: a small, poor country with a weak, corrupt or dishonest government.
a small country, run by corrupt politicians and they are usually dependent on one commodity

Example Sentences:
1.- If the current Prime Minister wins the election again, nobody can save our country from becoming a banana republic.
2.- “Trump was talking like he would become some dictator of a banana republic and throw [Clinton] and his political enemies in jail.”

Meaning: to have a great time. To live luxuriously.

Example Sentences:
1.- The team had a ball at the corporate event. Rarely are such parties so interesting for the employees.
2.- She knows how to have a ball by herself. She does not need a crowd to be happy.

Meaning: the initiative for taking action lies with somebody. To initiate an action now lies with the party that has the ball in their court.

Example Sentences:
1.- The entire family has stood by his decision to move to another country but the ball is in his court if he decides to change his mind at the last minute.
2.- I have already agreed to meet this guy to hear his proposal out but he did not show up in time, the ball is still in his court.