It is now telling me that it is over 10% done and that are "XYZ" blocks remaining. What does this mean?

The bitcoin network works by continuously adding new blocks onto the blockchain. Each block is full of transactions, and each transaction can be traced back to earlier transactions, creating a verifiable record of ownership for all coins in the system.

So to show your balance, the wallet needs to synchronize with the blockchain, so that it can accurately determine what (if any) coins you own.

And will my wallet be updated only when the synchronization is complete?

Yes, though if you want to find out your address balance more quickly, you could look up the addresses controlled by the wallet, and then use a block explorer website to check the balance of each individual address. Note that if your wallet has a large list of addresses, this may be a hassle to do.

Also, at towards the top of the wallet is there is a message "alert key comprised, upgrade required"

This message relates to the retirement of an alert messaging system that was built into the original clients, it is meant to alert you to the fact that the key that allows alert messages to be sent is now publicly known. This is not critical to the function or safety of the wallet.

If you upgrade to a newer version of the client, your sync time may improve greatly (depending on how old the software you're using is). If you post info about what version of the software you're using, someone may be able to provide more help in regards to this.