I do not know if just copying and pasting the wallet.dat (latest one in my current pc) and latest blockchain files will work just fine.
Also, I want to know how to generate or find the public addresses with my private address
To get a public address from your private key, go to the console within your wallet. Unlock your wallet if it is encrypted using:
walletpassphrase MyWalletPass 60
Then import your private key with:
importprivkey MyPrivateKey Lable
What each of those three words mean: Command - actual private key - what you want to call it
You can also get these instructions from the litecoin website. GAME is a modified litecoin blockchain.
https://litecoin.info/How_to_import_private_keys