if i buy a ipad pro in usa will i get full warranty In India?

1. If its the regular non-cellular / mobile data model, Warranty should be available in India. If its the cellular / mobile version the no. Warranty is only valid in the country of purchase.
2. No. Student discounts are country specific. As you must verify your student status in a participating university in the country of purchase.

Here is the link to look up the warranty terms:

Legal - Hardware Warranties - Apple

You can choose the device and country for specifics;however, but they all include the following terms:

IMPORTANT RESTRICTION FOR iPHONE, iPAD, APPLE TV, HOMEPOD, AND APPLE VISION PRO SERVICE.

Apple may restrict warranty service for iPhone, iPad, Apple TV, HomePod, and Apple Vision Pro to the country where Apple or its Authorized Distributors originally sold the device.

In Theory. The Apple Stores or Authorized service providers can still deny warranty service. Its up to them. Its just more likely for them to accept if its a Wi-Fi only model.