Does android store info like saved password securely ?
There is a class available in android for storing credentials - AccountManager. As well there is an open source application, that is storing user credentials with AES entryption on the device.
What happens if the phone gets stolen ?
hmm, then in that case I prefer to have 2 different application on device, which will monitor each other's state. If any of one uninstalled (Package removed) by abyone then it should wipe out all the secure data.