~Z~ Man
It cannot be related to maximum size per album because I can upload more in the same album.
It only uploads no more than 20 files each time, but I can have as many images as I want in the same album.
Has anybody tried to upload, like, 60 pictures at once?

There's no hardcoded 'number of images' limit in Ossn.
But there's a limit in every PHP environment named uploadmaxfilesize
and most likely the sum of your image file sizes are exceeding this limit.
Install the System Info component and click the sub tab Ossn Info in your left menu
Your current setting will be shown in the PHP Environment section and you'll get an idea.

I really don't see a problem uploading 20 at the time. But that's just me. I will dig up a code and see if there is a limit in there, not sure. I didn't see any on OssnPhotos. Thumbnails showing after refresh, that's just normal.

As for integration of Outside gallery. You will have to create one with the same user database "ossn_users". If you can find one with same table structure, than you're in luck. Otherwise it will require some modification to either gallery or ossn. Too heavy for my taste.

It does not say anything. It just counts the % at the bottom until upload is finished, and stops.
No error message of any kind that I could see.
The only thing I notice is that the thumbnails are not all displayed, but this might be a browser or display issue on my side as when I scroll or refresh then it changes. But the main issue is that it uploads only 20 images. Then again 20 next time and so on. As if a limit of 20 is set somewhere.
I thought of adding a separate gallary or file manager software in my site as provided by Softaculous, but access to it would be separate and I don't know if there is a way to integrate it in my OSSN access. :(
My PHP experience dates many years ago, so I don't feel confident to play with it.
Thank you for your care, Roman. Any hints are much appreciated.

What does it say when you try to upload more than 20 photos? Error? Message?