What is com.google.android.googlelogin

What is "com.google.android.googlelogin" and "com.google.android.googleapps"

Are these packages an official part of the Android SDK or something internal. I find it very difficult to find some documentation on them.

Furthermore, how can I interface with the built in gmail app if I'm not suppose to use these packages?

I can tell you that you don't need to interface with the Gmail application to do that. Unfortunately I do not personally have any experience creating email client so I also can't provide you with how to do that. You can find the source code for the "Email" application that is part of the system here. If you are willing to dig through it you can find how to look up unread message count. This may be more work then you're wanting to do though if you are just aiming to get a count.

You can use the Android Gmail Labels API to gain information such as unread email count etc.

https://developers.google.com/gmail/android/