How exactly does MyWallet's Android client work? When I create an account via my desktop browser, I am assured that the password only exists on my browser, and is not saved.

So, if I "pair" an Android device with MyWallet, can or can't I send BTC without entering the password?

How does this work with/without a secondary password? What if I first installed the Android app, and only then created a secondary password?

Are the files on my Android device / Dropbox encrypted with my first password? My second password? Both?
I think when you scan the QR code, your password is encoded in that barcode, so your Android phone stores it locally.

I haven't tested it myself, but considering this I think you have to enter the secondary password to your Android phone as well. It will either require you to do it every time you make a transaction or remember it for you.