Hi,
If you look at the PayPal payment on your PayPal account, you should have an "invoice id" which corresponds to the order ID in HikaShop. So I would first recommend to check this.
Also, in Customers>Emails history, you can check the emails sent by HikaShop.
It's possible that the order was created and the emails sent by HikaShop, but they weren't delivered by your hosting email server because of spam related issues.
Also, you said that some users got errors with authorize.net
Does that mean that for some users they are able to pay with authorize.net ? What error did they get exactly ?