Tried using the blockchain.info app on my phone to import a private key from a paper wallet, but looks like that functionality doesn't exist in the app - only scanning addresses to send to.  Does anyone know of an android app that allows importing paper wallets, or do I need to lug my laptop and webcam around if I ever want to load up a paper wallet for spending?

Why not keep both backups on your USB stick, that way you'll ensure that you have all of the addresses from each time the wallet was backed up, and not risk old addresses not being in the new backup?

In your client, you should be able to get the transaction ID's for each of the transactions you made.  You can then go to blockchain.info and paste those transaction ID's into the search box.  You'll probably see that the transactions you made are either unconfirmed or have some small number of confirmations.  If the transactions were small, and you didn't add any transaction fee, it may take many hours for those transactions to be accepted into a block.  However, as soon as those transactions are accepted into a block, they'll have additional confirmations at the normal rate (that is, blocks will be piled on top at the usual 6 blocks/hour or whatever they happen to be mined at).  Hope this helps!

Read this:
https://en.bitcoin.it/wiki/Securing_your_wallet

Yes, all you need in order to send money is the public address.  You could even send money to public addresses that don't exist yet! (well, technically they all already exist, just nobody knows the private keys).  Don't do this though, you can't create a private key from a public address - that's the whole point of the cryptography.  Anyway, create a new wallet offline with bitcoin-qt or some other client, generate a new address, and then use blockchain to send money to that address.  Make sure you back up the wallet that bitcoin-qt generates though - once its lost it's gone for good!