Is there any way to integrate the private keys and addresses from the old bitcoin-Qt to Amory's deterministic wallet, so that I can just have one neat file without having to constantly backing up the imported private keys? I'm still expecting payments from a lot of these addresses, so I actually do need to import them instead of just generating a new one in Armory.
I also want to import vanity addresses, can these be integrated into the Armory's wallet without having to frequently backup this imported key?
As long as you don't use the Satoshi-Client or another non-deterministic client to spend the coins on these addresses you don't need to back the keys up again. The other client's wallet IS in fact a backup, you can spend funds from the imported keys as well as from the "original client".
The Armory wallet backup does NOT contain keys imported later, but writing down each imported key and safely storing the paper is sufficient as a backup. Keeping the wallet where the key was imported from on another storage is also a backup.
Example:
1) You have 2 BTC on your Bitcoin-QT address.
2) You import (not "sweep") the private key into armory.
=> You will see the same balance in both clients and can spend the BTC from both, but spent funds will vanish also from the other wallet on blockchain update.
3) Now let's assume you spend 1 BTC with Bitcoin-QT.
=> Bitcoin-QT will have a balance of 1 BTC left.
=> Armory will show 0 BTC afterwards.
This happens because the whole balance is sent, and the change of 1 BTC is transferred to a hidden address internally generated by Bitcoin-QT, the remaining balance will not remain on the originating address. The Satoshi client's GUI won't show the addresses/keys where parts of your total balance are currently "stored".
4) If you now use the command line interface of Bitcoin-QT to look up this hidden address and export its private key, you can import this one into Armory as well.
=> Now your remaining 1 BTC is available in Armory again.
You must back up each private key individually, unless you generate it from an Armory wallet.
So you will know when a new backup/import action is needed, because in this case the balances in Armory and the other client differ. You can hold the addresses of different origins grouped separately in different wallets in Armory, so you see possible differences easily.
[Edited because of typos…]