@ricardoherrera994 Thank you so much for your amazingly detailed answer! Needless to say, you solved most of my doubts! 
Even though the screenshots were in Spanish, I surprisingly understood them all!
So it turns out that the Wix Pro Gallery (for the time being) does not allow either tagging images/videos or searching them 
As you can see, these are still feature requests. It is to be noted that you can search images from the Media Manager but unfortunately, that is of no use to me since I want the user to search for images on the live site.
I don’t know why they haven’t added these two crucial elements to the Wix Pro Gallery. I’ve voted for these features and I will also send an email to progallery@wix.com and urge them to add these features as soon as possible. I will also post about it to the Wish List to draw the team’s attention to this.
Using the Content Manager to tag images/videos is indeed a good idea and fortunately, I’m familiar with it too, but it doesn’t sync media to the Wix Pro Gallery’s Media Manager.
So what I’ll do is I’ll wait for the Wix Pro Gallery team to add these two features and, till then, I will create a library without these two features (at least for now). But I hope that these two features will be added soon.
Thanks once again Ricardo for spending so much time and writing a very detailed answer for me! Also, thanks for adding the screenshots (even if some of them were in Spanish! XD) I really appreciate it! (: