1. Making a copy of 'wallet.dat' is sufficient to recover a wallet, assuming the copy was made before any problems started?
Yes, as long as the copy is made while Bitcoin-Qt is shut down and not accessing the file, and as long as the copy is made recently. Bitcoin-Qt creates a new address every time it sends a transaction. It also creates a new address every time you click the "New Address" button. When you create a copy of wallet.dat, that copy already contains the next 100 addresses that Bitcoin-Qt will use. If you made the copy a long time ago and have used more than 100 addresses, then your backup is no longer sufficient.
2. Once a fresh install of Bitcoin-QT has been made, replacing the new 'wallet.dat' with the copy/backup 'wallet.dat' will load all data that was in the copy wallet?
This is generally true. Occasionally, you may need to start Bitcoin-Qt with a rescan command line option to get it to scan the full blockchain looking for transaction history. In some extreme circumstances, it may become necessary to delete the blockchain from your computer and wait for it to re-sync completely from the beginning again.
3. At this point, my assumption is that somehow it's going to sync again and update any transactions in your wallet that you made since the backup?
Correct. That is the intended design.