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Without an agent doing work, heat will always flow from a hotter to a cooler object. Two objects of different temperature always interact. There are three different ways for heat to flow from one object to another. They are conduction,convection, and radiation
^^Answer for 3 and for question 4 is

The hot cup has more air flowing around it to cool it down
meanwhile the cold cup has COLD air flowing around it so it would jst do nothing in a result of the cold cups cool temputure to increase 

I really hoped this helped and have a great day :)