"Unique Product Serial Number " is essential for maintaining "Warranty Management" - Is it true?

yes true

That depends on the type of product you are considering. It is essential for products like computers and machinery. It is not the same for products like software packages for example which is more managed by a version identifier rather than a product serial number.

Yes it is required. in order to track a product and mainly for the company purpose

Yes it is true

 Because it is considered the ID for the product

Its easy to manage and track, when you have a unique indentification number.  It depends on the type of product you are considering and changes for company to company. 

Yes it is  

Yes it is the most effective for the warranty management.

Yes, because you will want to know the status of the warranty for that particular product/item. Then you may internally group serial numbers by lot for example in order to detect manufacturing defects.