Please do simply as advised and install ossninfo.php

Aside from that: The Facebook theme IS marked not to work with the latest OSSN version.
So please change to Goblue, or another working theme.

OSSN installed: https://ultimatrompeta.com/chat/

I installed OSSN manually. There are several issues, but the main one I'm concerned is that it won't let me ADD GROUP. Instead, I get this message:

Cannot create group! Please try again later.

The other problems are:

1) When Flush Cache is used, I get a blank page. The flush functions well, but I would have open another page in order to continue. The URL I receive is this:
https://ultimatrompeta.com/chat/action/admin/cache/flush?disabled=disabled&ossn_ts=1582216213&ossn_token=266b8b213ac1761299a6be92a6503dfc

2) I used to get a 500 (= internal server error), but my hosting provider (Hostgator) fixed that issue.

3) The other issue is that a user or even I (administrator) cannot LIKE a post comment/picture/video. We can comment on any post, we can like or dislike any comment on any post, we can upload a picture comment on a post, but we're unable to like the post itself.

I'm using a Toshiba Laptop with Windows 7 x64, fully updated.
Browser used to check work: Chrome (fully updated), Firefox (fully updated).

Please do as advised in
https://www.opensource-socialnetwork.org/wiki/edit/1101/how-to-report-a-bug-error

According to Hostgator everything is OK. Here's their response:

At this moment I have confirmed that your database has all the necessary privileges for any modifications needed. As well I went ahead and ran several checks (to check if the database is corrupted or locked) on the database and no issues could be detected with any of the database tables. To move forward I also reviewed the site error logs and could not locate any errors that would indicate there to be an issue on the server side.

In order to move forward with trying to provide the best support possible, I research for any possible issues reported for this software: OPEN SOURCE SOCIAL NETWORK specifically with not being able to create groups and located the following forum:
https://www.opensource-socialnetwork.org/discussion/view/410/creation-of-group-problem-in-my-site. However, if we can receive specific instructions on how to replicate this issue and temporary login credentials to the section where this is taking place we can definitely attempt to provide a solution to the issue.

¿What should I do?

I'm on a shared business hosting.

There must be something wrong with your database.
Did you tried to fill name in alphanumeric ?
Try to see if any table in your database is locked or corrupted.