Hi,
When you login via the joomla user login module/login form, there is no reason for joomla to redirect to the checkout, if that's what you want.
However, if you log in via the login form of the checkout, you should indeed stay on the checkout after the login.
If that's not the case, then it means that the cart is lost during the login process. There are two possible reasons for that:
1. You unpublished the user synchornization plugin of HikaShop via the joomla plugins manager and because of that the cart cannot be kept during the login process. So if that's the case, please publish it back.
2. You have a user session handling issue on your server. Try to change the session handler in the configuration of Joomla and see if that helps.
Regarding the item still after after deleting it, there are three possibilities I can see:
1. You still have some caching activated on your website. Please check that the caching plugin of Joomla, the caching configuration option of the joomla configuration and potentially the caching option of your template are all turned off.
2. There is a mysql query error during the delete process which prevents HikaShop from deleting the product. Turn on the debug mode option of the joomla configuration and try again. If you have a mysql query error, you will see a big error message when deleting the product.
3. You have some SEF issues on your website. Try again with the SEF option of the joomla configuration turned off. If that helps, then that will require that we analyze further the issue.