Error 500's could be the result of many things. The links you've provided in your research may have had 500 errors but in briefly reading through them ... the first is very old (which is why that thread is locked). The second and third links provided had different problems although showing error 500's ... and different solutions.
In your case, this is key:
"Cannot find session record h25kg7hhk122f7d26rp45l40l6 for user 97, creating new session or similar.
which indicates that you are using database for sessions, as opposed the recommended 'files.
Login to moodle and in the site admin search box type: session.
Find the setting for sessions to use database and change to files - ie, turn off using database for sessions.
That might kick you out of your session as the next click on anything would check for a session file and there isn't one there yet for your access.
Check your moodledata directory ... there should now be a 'sessions' directory and contained therein a file ... which is a session file for a user.
Also, check how often your server is running the cron job/task ... recommendation now is every minute. One of the task in the cron job is a check on sessions and to clean up stale session files found in moodledata/sessions (once you switch from DB to files). If you don't change sessions to files and leave it for DB, that could be the problem ... task can't update the records fast enough or at all if DB server is struggling.
As far as desire to have X number of users in system taking quiz/questionnaire at same time, that relates to several factors in setup of server. The major one being the number of connections allowed to the DB for the Moodle ... which is a mysql setting. Not set in Moodle, but via whatever you have for MySQL in cPanel ... IF that is even there for you may not have a package with the hosting provider that allows you to tweak such settings ... if you are on a shared system.
So a little more info about server is in order ..
How are you hosted? shared/VPS/other
How much memory does your server have OR been allocated?
Etc.
'spirit of sharing', Ken