Do I need to pay fees for the transactions from my full node? I have a full node running right now.
I've created a wallet on my server. Do I need to define any transaction fees while transferring my coins to another wallet? lets say to a wallet on blockchain.info?

Thanks.
Yes. All transactions should pay a transaction fee. Running a full node does not give you any special ability for you to not pay a transaction fee and still have your transaction confirmed in a timely manner. Your wallet should take care of setting the transaction fees for you.