Hi,
1. I understand that you get that error that the end of the checkout after you click on the "finish" button.
Both points indicate that the "finish" process takes too long on your website. However, regarding the processing of HikaShop, unless you have some strange order mass actions configured, there is no reason HikaShop would take so much time for that. It should be over in 2 seconds. However, on some servers, HikaShop has to wait for the order notification emails to be sent by the email server and it's the email server which takes a lot of time sending the emails. Or it's possible that you have some plugin trying to connect to an external service and the access is blocked and thus it has to wait for the timeout of the connection.
To check if it comes from the emails, it's easy. Go in the menu System>Emails, disable all the emails and try again. If it goes fast, then the problem is with the email server. If it doesn't change, then the problem must be linked to a plugin, and you can start disabling them one by one and testing each time if it helps in order to identify the one causing the issue.