How do I tell whether an app or website has accessed my account password? Is it possible for apps to access one's Google account login credentials? How can a user determine whether this has occurred?
To determine if an app has accessed your account, you would need to look at that service.

For example, too see if an app is connected to your Google account, while logged into your account in a browser go to https://myaccount.google.com/permissions and you will see all the connected apps, what they are connected to and if they have basic account information permission or not. 

Facebook has a similar page available at https://www.facebook.com/settings?tab=applications as does Twitter at https://twitter.com/settings/applications

Other services you may have given an app credentials to likely have a similar page, if not I don't believe there is a way in your Android device to see if an application has actually used any permission or credential you have given it.