Hi Ian,
I have to agree with Pavel, as always so far ;)
In most cases, if you used Joomla for at least 2-3 months before, you don't need Helix QS, just install raw Joomla 5.0.x then install Helix Ultimate template + all needed extensions one by one. QS demo was created for training purposes only, for "green" beginners.
And No, you cannot install QS inside current Joomla website for obvious technical reasons. It must be installed similar to Joomla, by installing step by step.
If you need good looking pre-made page themes, just use "Page Layouts" >> https://www.joomshaper.com/page-builder/layouts
Error 500 can be caused by many things, server settings, rules in .htaccess file etc.