Hi,
1. If you don't send the notification is it fast ?
If so, then it's probably that the communication with the email server is slow. It's the same at the end of the checkout when you click finish and HikaShop sends the notification emails. HikaShop's processing there is really fast. What's slow is the sending of the emails and then the redirection to the payment gateway (done by the payment gateway).
If you disable the emails and use a "collect on delivery" payment method where there is no redirect, you can see the real speed of the finish process of HikaShop ( + the processing of the thank you page by Joomla and the template of course).
If it's not fast even without the notification, then it means that it probably comes from another plugin, which does things when the order is being modified or a mass action.
2. You mean that you copy once a product and it's slow, and then you copy the same product again and it's fast ? In that case, it means that your hosting has some MySQL query caching system which allows the process to go faster the second time.
It also means that your product has a lot of variants or that there are a lot of elements.
A variant is stored like a product.
So if you have 100 variants for each product and you have 1000 products, that means that you actually have 100 000 entries in the hikashop_product table. So with variants the tables can easily grow big leading to the MySQL queries getting slow.
To check that, go in your PHPMyAdmin and open the table hikashop_product. You'll see there how many entries you have.
With a few 10s of thousands of entries it should be fine on any server. We've seen HikaShop working with a few millions entries in that table on a powerfull server.