Hi,
First, check that the "order admin notification" and "payment notification" emails are enabled in the System>Emails menu.
Then, check the Customers>Emails history menu. There, you'll see all the emails sent by HikaShop.
It's possible that HikaShop sent the email to the email server of your hosting, but that it couldn't send the email for some reason, or that it was flagged as spam and discarded.
For example, if the recipient email address and the sender email address are the same, it's possible the email server refuses to deliver the email to the inbox. Some email servers allow for it, some don't.
If the email is in the history, you'll have to check with your hosting company support for the reason why the email could not be delivered. The log of the hosting email server will contain the information so they'll be able to tell you if they check it.