Thanks for the screenshot: this should show the images in the zipfile. Please try the attached zipfile and note that it shouldn't be a zipped folder structure, just images zipped together.

Thank you. The test zip uploaded and worked as it should — the first time.

So that's good, something is working...

I then tried to replicated my test original files in photoshop to match your test files>
rgb, png, 50k size, all in a zipped folder but couldn't get a successful upload — same error as originally reported.

Allowed image types are jpg, jpeg, gif and png. However, other image types should result in an error message.
As for the zip file: don't zip a folder, but the contents of a folder (without subfolders).

Fatal error: Class 'rsgImagesItem' not found in /home/scenestr/public_html/administrator/components/com_rsgallery2/includes/img.utils.php on line 416

At the point were you get this error message, the original, thumb and display images already have been deleted. There is only the database entry left to delete. My first guess with this error is that perhaps one or more files aren't installed, and that reinstalling might help. You did that.

I then re-uploaded your test files which worked again, however now they cannot be deleted. Trying to delete them returns a an error:
500 - and error has occurred

Can you turn Joomla's Debug on (Backend > Site > Global Configuration > System > Debug System = Yes) and set Error Reporting to Maximum (Backend > Site > Global Configuration > Server > Error Reporting = Maximum) to see what more information you get on the Error 500 message?

Additional questions
1 - Are you using SEF, if yes, only Joomla SEF (and then what is RSGallery2's advanced SEF option: Backend > Components > RSGallery2 > Control Panel > Configuration > tab: General, Setting: Advanced SEF) or what third party SEF?
2 - What is your MySQL version?
3 - Are you logged in as a Super Administrator?
4 - Did you upgrade to RSGallery2 3.1.0 or was it a new installation?
5 - Can you go to Backend > Components > RSGallery2 > Control Panel > Maintenance > Consolidate Database. That'll give you a list with all item "where something is not completely right", for example a missing display/original/thumb image or a missing database entry. For each line there is a link to try to 'solve' that problem. Does that help for any existing problems?
6 - What browser are you using?

A lot of questions for a strange problem...

Some weird things are happening...

As for the images, you now have three images in your RSG2 directory and you seem to have entries without images (e.g. 01.jpg.jpg is not a thumbnail on your server, however, it shows up in the gallery. I was hoping that with the Maintenance-Consolidate you could remove such an entry (which I've done myself numerous times while testing different things).

I also get this error on your website where is seems that sh404sef is working hard on something and doesn't get it done within the memory limit (and that limit is high for I am used to, but perhaps shumisha from sh404sef might have a different experience?):
http://scenestr.com.au/1-01.html
Fatal error: Allowed memory size of 33554432 bytes exhausted (tried to allocate 76 bytes) in [...]/administrator/components/com_sh404sef/sh404sef.class.php on line 2694.


On the Error 500 you're getting:
JDatabaseMySQLi::query: 1062 - Duplicate entry 'Backsliders.jpg' for key ...
It seems that there is already in image with that name in the database. Normally RSGallery2 handles duplicate names. I've uploaded my "test images" over and over again with zip files, each time they have the same name, and I've never had a problem with that. At this point I don't understand why RSG2 isn't handling the duplicate file names.

What I'm hoping is that somehow with a specific set of circumstances things went really wrong. Since you seem to be "just" at a testing stage I would completely removed RSGallery2 from the system and then reinstall it. How to do that?
1. Uninstall RSGallery2 like you normally uninstall a Joomla component: Backend > Extensions > Install/Uninstall > Components > Select RSGallery2 and click Uninstall. This removes all the files.
2. Find the directory /JOOMLAROOT/images/rsgallery/ and remove this directory and its contents
3. Remove the RSGallery2 database tables, there are five of them: jos_rsgallery2_acl, jos_rsgallery2_comments, jos_rsgallery2_config, jos_rsgallery2_files and jos_rsgallery2_galleries (where I've taken "jos_" as a database prefix, which is gx8s3_ in your case, based on the error message). This can be done with phpMyAdmin or DBWebadmin or any other program your webhost offers.
4. Reinstall RSGallery2

It's always best to have a full backup ready of your website (files and database) before making (big) changes.

What I'm hoping is that this will get you started in the backend, being able to upload zipfiles (not containing folders, only containing images) and being able to remove items as well. Your database, php version etc. seem perfectly fine.

I haven't been able to prevent the image name from publishing (screenshot). I have turned off just about every option but it persists. Is this possible?

Please disregard. Have just noticed this topic is addressed elsewhere.