I love going to the farmer's market. I haven't in a long time, but I used to buy raw milk there straight from the farmer.
Why is it called farmers market.Does it mean its exclusive to farmers only?
It is called a farmer's market because consumers can buy products directly from the farmers in a physical retail marketplace.
OK, ,when was the earliest history of such markets?
Forms of marketplaces like this existed before the Industrial age, but were often part of a much broader market where suppliers also bought their goods.
That good.Is it regulated by the government or is it a free and open market operations?
I'm not 100% sure of the details, but due to their nature they do tend to be less rigidly regulated than your typical retail shop for produce. 
So what are the major items of sales at the farmers market?
Typically you can buy things such as  fruits, vegetables, meats, cheeses, and sometimes prepared foods and beverages. I've even seen thing such as homemade soap for sell at them too.