If you ever get a message about target "android-xx" was not found. Check to see if the Android SDK for level "xx" is installed first and also ensure that you have the Build-Tools version for that level as well. Additionally, if that doesn't work, recall that Android Studio uses a different SDK from the default Android SDK. Android Studio installs their SDK in the android-studio\sdk folder along side the other Android SDK. Check the default SDK to see if that one is missing the afore mentioned components.
After checking all of that, try using the Invalidate File Cache and Restart option from the File menu in Android Studio.