I have received an award letter of a scholarship which has terms and conditions to be printed on a non-legal stamp paper. There are 4 pages and at the end of each page there are the terms "Scholar Initial" and "Guarantor/Surety Initial" side by side with a short blank line above each, indicating that something needs to be written on it. What do they mean and what should be their purpose?
It means that the scholar (presumably you) and the guarantor/surety should each write their initials in that space, i.e. the first letters of their first and last names. John Smith would write "JS".
This is a common way of acknowledging that you have read and understood the text on the page.
"Guarantor/Surety Initial" is typically an someone (specifically, an adult) who guarantees to pay money back if the terms of the contract are not met.
In your case of this scholarship, the people who offer the scholarship will probably want their money back if you drop out or flunk.
If you're a minor -- or even a young adult dependent on parents for tuition, etc -- then the Guarantor will most certainly be your parents. If you're financially independent, then you might be the Guarantor.