Why is there separate private key for every adress? What should i record for my paper wallet? Why is there separate private key for every address in Litecoin? 
What should I record for my paper wallet?
Why is there separate private key for every adress in litecoin?


Because that is how public key cryptography works. Each address is the hash of a public key, and each public key only has one private key. Thus each address has its own private key.


  What should i record for my paper wallet?


The private keys of your addresses. You should really only be using paper wallets for long term storage. They are not very good for doing transactions.