Is Apple Push notification using APNS free of cost?

Apple does not charge a separate fee for utilizing the push notification service.

Your only cost is a server that will be sending the push notifications to Apple. There are third-parties that provide this servers and there is a fee for that.

Answer for your question 1,2 and 3 is: Apple doesn't charge you for APNS - but you have to maintain a server for pushing.

Try these third parties for pushing,

• PushWizard, a free and unlimited push service.

It can send 250 million push messages / hour and PushWizard is free for unlimited devices, while other services can be very expensive if you have more, than 1 million users to reach at least ONCE per month.

• Monopush, which provides a RESTful API and a lot of free push alerts up-front to handle the server infrastructure for you.

You need just copy and paste a few line codes to inside of your application and then magic will be started. After that you can start to watch, analyze, categorize your clients and you can send push messages to them as well as resource messages.