My first transaction using Bitcoin-Qt I used Bitcoin-qt (Bitcoin Core) on desktop to create a wallet a while ago and I'm a little confused how it works. 

I never fully "synchronized with the network" I'm assuming that means download the entire blockchain. I'm about half way there and 30gb deep. I created an address to receive a transaction but don't have a balance in the wallet. I'm assuming it's because it's never caught up with where my transaction is on the blockchain. Is this correct?

I can see when I take the address and look it up online the transaction of receiving the funds I just can't confirm a balance.

It doesn't seem that there's any password that I ever put in either. When everything does sync can I only transfer my balance out using the same app?

Also I had to replace my hard drive on my mac recently so I took both the Bitcoin app and the Library/Application Support/Bitcoin folder and put them on my new hard drive, are there any other files I would need to get access to my balance?
I'm assuming it's because it's never caught up with where my transaction is on the blockchain. Is this correct?


Yes.


  I can see when I take the address and look it up online the transaction of receiving the funds I just can't confirm a balance.


That's normal, if your client is still synchronizing.


  When everything does sync can I only transfer my balance out using the same app?


No, it's possible to use a different Bitcoin wallet. You need to 'export' the keys in your wallet to another program. See How can I export the private key for an address from the satoshi client?


  Also I had to replace my hard drive on my mac recently so I took both the Bitcoin app and the Library/Application Support/Bitcoin folder and put them on my new hard drive, are there any other files I would need to get access to my balance?


Is there a file inside there named 'wallet.dat'? If yes, then you have what you need to spend your Bitcoins. If no, then no.