Hi,
I couldn't find how to access your checkout on your website.
Could you provide the precise procedure to replicate the problem ?
If the page processes for a long time before failing, it usually means that there is a problem with the sending of the emails. HikaShop sends an email, and wait for the email server to say if it's ok or not, but the server hangs in there, without answering. So HikaShop waits, until the maximum execution time of your PHP is reached and the page processing crashes.
Try to deactivate the different emails in the menu System>Emails and see if that helps.
If it does, then the scenario I talked about above is highly likely and I would recommend to check your email settings from the HikaShop and Joomla configuration with your hosting company and maybe have them check the log of their email server for clues on why the email server does that.
If you still get the same error without the emails, then the problem is elsewhere. Check that you don't have mass actions enabled (menu System>Mass actions). Otherwise look at the PHP error log of your website. It should contain a fatal error message corresponding to that 500 error and which will provide more information on where the problem is coming from.