I was told different things by different dealerships. One of them said that 150-point inspection is just safety and it doesn't qualify for additional limited warranty of 12month after the factory warranty expires. So only 160-point inspection qualify for this warranty?
Second told me that it's opposite and third that both 150-point and 160-point inspection qualify for additional limited warranty of 12month after the factory warranty expires.

Which one is right?

 

Did they put anything in writing?

Is it their own warranty inspection or a Nationwide Mazda Warranty?

 

No one here can tell you what or how someone else's warranty works.. we can only give opinions.. The dealer would probably have the greatest clue on how something like this works . .

 

One dealer is shaving points like he plays in the NBA.

 

I'm sorry to hear someone who is selling a car is also confusing you. For a moment let's imagine that the confusion is not intentional - because that generally does not help to sell a car. Hopefully you understand:
You can purchase an extended warranty or a dealer can choose to provide an extended warranty (it is built into the price of the car). An extended warranty has nothing to do with the number of inspection points. BTW if you purchase a car expect that you will get mail from vendors wanting to sell you an extended warranty.
A separate question: Should you worry about getting or actively look to buy an extended warranty? Most people would say "no". The companies that offer these warranties have done the math and considered the probability for a specific car and mileage whether or not they will have to pay you for repairs that are covered. They rarely lose money on the warranty. The best advice is to save some money for repairs and be your own extended warranty. But everyone is different and extended warranties offer peace of mind - so no judgement from me.
However, sellers of extended warranties know that people are most likely to buy when they feel economically vulnerable - like when signing papers for a car loan.

 

Now that was WELL SAID !!!