Ok, so one question at a time ...
First of all, about file size and dimensions of images on your website. This is something that all gallery website owners need to consider up front. If the purpose is to simply showcase the images to the visitor, then you should optimize the images for viewing from the web. I already wrote a post specifically about this:
https://www.photo.gallery/blog/image-size-quality-photo-gallery-websites/
Essentially, your images are too big (3-4000 px), and this is mostly a waste, because your visitors screens will shrink down the images anyway. By resizing your images down to for example 2000 px (still high quality) and saving with some compression (not generally visible), you can convert your 2-3 MB images down to 3-400 KB ... They will load much faster in browser of course!
Basically, you should either resize on your desktop BEFORE upload, or resize in the same process as uploading (when using the Files Gallery uploader, there is an option to "resize and compress"). There is no need to store multiple sizes. You simply store the large size that is optimal for viewing from the web. You can keep your originals locally, on your desktop ... Besides, it's better that you don't offer large original images directly to your visitors.
There is no "structure" or any change you need to make. You simply upload the optimized images instead of the originals, which are too large.
Olivier Another thing : I have paid the licence and installed the number into the _files/config/config.php file. But I can see a very little mention of "files gallery" under my galleries. Normal ?
I checked the website you linked to, and I can see this is Embed gallery, which you don't have a license for. You have purchased a license for Files Gallery, which is used as the backend API (engine) for Embed. You don't actually need a Files Gallery license to use Embed, unless you are going to edit/manage/upload files from the Files Gallery interface. Effectively, if you want to use both Embed and Files Gallery without limitations, you will need a license for both of them (2 x $39).
Let me know if you have further questions.