First, we can verify or validate the transaction on the website. I don't understand why do we need a full blockchain if we are not mining.
What website? There's no website that defines the blockchain. All blockchain explorers just show the information. If you are relying on a website to check that your transaction is valid, then that is a central point of failure. What if whatever website you are using mistakenly says an invalid transaction is valid? Do you just blindly trust the website? This has happened many times in the past, especially with blockchain.info.
The whole point of the blockchain is to remove central points of failure and to remove trust in third parties. Relying on a website to tell you what is correct defeats that purpose.
Second, doesn't miner verify the transactions before including into the block? In addition to that, the process of validating the block served like a double validation?
Miners are supposed to verify transactions before including them in a block. Just because they are supposed to verify does not mean that they actually do. Just accepting a transaction that has been included in a block does not guarantee that the transaction is valid. What if a miner included an invalid transaction?
Again, the point of a blockchain is to remove trust in third parties. By trusting miners to have validated transactions, you are trusting a third party. Verifying a block after you receive it from someone else removes that trust in a third party because you yourself has checked that the block is valid.
Third, when the block is added to the network, isn't it a third validation?
Forth, when the block has several more confirmations, isn't that a forth validation?
Kind of (to both). But again, you yourself are not verifying the blocks if you are not running a node. You are trusting that someone else has verified the blocks. That is trust in a third party, which is what the blockchain is designed to avoid.
A light node, although doesn't have the full ledger since the genesis block, keeps a section of the most recent blocks, isn't that sufficient?
Why would a light node be riskier?
No. If I had sufficient hash rate, I could produce a block that has an invalid transaction and send it directly to your light node. This block with the invalid transaction that spends a nonexistent input and could be something that defrauds you. If you have not verified the entire blockchain and constructed the UTXO set, then you do not know that the transaction is invalid because it spends an nonexistent input. You cannot verify this for yourself. You are trusting a miner that the transactions is valid. This is riskier because you could inadvertently accept an invalid transaction and thus lose money.
Realistically, what are the chances of receiving incomplete or invalid blocks?
Pretty low. But the whole point of the blockchain is to remove centralization and trust in third parties. By using a light node, you are now trusting third parties and this increases your risk for being defrauded.