I am a developer. these days we are going to jump into Crypto well. So i have read lots of blog online how Crypto currencies works. But i am little confused for the private key.
1) Where it is stored in decentralised ledger.
Private keys are not (and should not be) stored in a decentralised ledger. The Blockchain (aka "The decentralised ledger" as you've called it) is public and simply records reassignment of "ownership" of bitcoins from one public key to another.
Private keys are exactly that... PRIVATE... they are not meant to be shared and should be kept safe, secure and guarded appropriately.
2) How it is validated while sending payment to any other key.
When attempting to transfer coins from a public key to another public key, you prove "ownership" by cryptographically signing the transaction using the appropriate private key that matches the public key you are transferring FROM. The various nodes will then check that the signature provided matches the public key. If it does not (ie. the transaction is not signed, or signed with the incorrect private key) then the transaction will be rejected by the network as invalid.
Note... you CANNOT derive a private key from a signature that has been put on a transaction.