If you have an immovable object on a table, and you remove the table from under the object, like in the tablecloth trick what will happen to the immovable object? will it fall? isn't it immovable? will it just float there? what about gravity?

It will not move because you said it is immovable which is immpossible but if it really is unable to move no matter what then it wont move but logicalls if it was real yeah it would move, because of ghravity.

compass can be used day and night, cloudy or sunny

the moving of the box is a result of centripetal force. think of that  as a car or a truck in this case creates a turn, the force of friction performing upon the turned wheels of the car runs centripetal force obligatory for circular motion for the things inside it.