1. Your understanding of the Vat is correct i.e., We take the credit of the VAT we pay on purchases and Debit the VAT amount we collect on sales.
VAT on sales (-) VAT on purchase = Net payable VAT
In other words VAT is payable only on the value addition made by the dealer.
2. When invoice is raised by any seller he show the price and Vat seperately
In your case selling price does not bifurcate the Price and vat, which means it is inclusive of the VAT. SP will be 1+.21=1.21
So to understand the formula Y-(Y/1.21)
Where y means Sale price
Y/1.21 means the price of the fuel
if 1.21 = 42 or 756000
So to find 1.00 = ? (which is price in your case)
(42*1)/1.21 or (756,000*1)/1.21
= 34.71 or 6,24,793.39
So the vat = 756000-624793.39 = 131206.61
As your CA does not have clear bifurcation he is using this formula.
3. Taking credit on cess is a debatable matter refer different case laws & notification, and recovery of licesnse fees is concerned you can deduct if you can bifurcate the same from the Sale price.