As a fairly new user to an Android smartphone myself, I've often wondered about the difference between 'Photos' and 'Gallery'. Your post has spurred me into asking that nice Mr Google to explain things for me, resulting in me finding this:
https://www.androidcentral.com/gallery-or-photos-android-which-should-you-use
(You might also find it worth a read).
If an app simply does something on your phone (like deleting unwanted pics) then it won't use any of your data allowance. However if it uploads something to the cloud, or downloads it from there, it will use however much data the picture takes up. That will depend up how many megapixels the phone's camera has got and also on any relevant settings for that camera. However, as a very rough guide, a photo taken using the best quality settings on a top-of-the-range phone might have a file size of around 8 MB, whereas a more basic camera on a cheaper phone might only produce images with file sizes of around 2 MB.