Transfer BTC from online wallet to paper wallet
My paper wallet will still be secure? because i've only used the public key online - correct?


Sure, if the wallet was created securely in the first place then sending to it's public key (address really) poses no threat to it. 


  How can I confirm that the BTC's are in my paper wallet? 


You can use a block explorer like blockchain.info or blockexplorer.com to check the balance of your paper wallet address. 

Might not hurt to do a trial run with a small amount first.