Does sending images on Google Hangouts (Android application) count towards my Google account storage space?
I don't see why it would, but right after sending some images via Google Hangouts I received an email regarding my Google account storage, so I wonder whether this is a coincidence:
Yes, all the images which are sent via google hangouts are stored in your account storage. Refer this link to see all of your account storage on Google Dashboard. Click on Gmail to see stats. Click on chats to see all of your images.
Take this image as a reference.