Hi,
Well, the problem is that the errors you provided before ( on this message
www.hikashop.com/forum/install-update/90...to-5-1-0.html#365148
) are normal MySQL queries which should not fail.
These are Joomla MySQL queries, and are not even related to HikaShop.
Also, the error message itself usually happens when the MySQL server is too strained, and because of this, it can't process the MySQL queries anymore.
And since that happens during the installation of an extension, it probably means that the limits imposed by the hosting on the MySQL queries are too great for the important processing needed for all the MySQL queries run by the Joomla installer during that process.
So, that means that even if you provide a backend access, there is not much I'll be able to do. If you reported the issue to the hosting and they were not able to do anything, I suppose you'll have to change your hosting to something a bit more beefy or better configured to be able to support the load during updates.