How to see Gmail labels on the actual emails, in Mail.app? Is there a way to view the labels from Gmail in Mail.app on an email, while the email is in the inbox, without opening the actual email (like in Gmail)?

The image shows the emails labeled as K, D, and S (on the right bottom corner of each email):


This image shows how there are no lables shown on the actual emails, while in the inbox, in Mail.app:
So, check the following in Gmail:

Open up Gmail 
Click the gear in the top right to open settings 
Goto 'Labels'
Ensure the 'Show in IMAP' checkbox is ticked next to any labels you wish to see as folders in Apple Mail.

I hope this answers your question, and that this is what you where looking for.