The passwords are stored in a file on the phone after some obfuscation. For someone to get user's password stored by ReaderScope, they will have to go past following three steps:
1. In the Android framework, no app (or user) can access any other apps' internal files. The obfuscated password is stored in one of such files by ReaderScope. However on a rooted phone the person with physical access to the phone (and know-how of Android SDK) can reach to such file.
2. If someone opens the file, the password found will look like a string of numbers and characters which have no resemblance whatsoever with the original password. This is however not an unbreakable code. A knowledgeable person, can figure how to decode that string. It merely protects from accidental disclosure of user's plaintext password, in case the file is opened unknowingly.
3. If someone decodes the string, the result will be a jumbled form of actual password - an anagram. The jumbling is hard coded in the app. But it's not super difficult to break an anagram.
From the above three steps, step 1 is the strongest link and is under user's control. If anyone has suggestions for more secure mechanism, I am willing to consider.
Yes, the login with Google happens over https. That's the only supported mechanism by Google.