Hi,
First, your template include jQuery more that needed which create some javascript errors.
It could explain that some javascript is not running in the page so, some messages are not displaying.
After that, the alert boxes on custom fields are managed by the form itself, not the custom field elements.
The address form checks his values before the submit, the "add to cart" might not.
Regards,
Jerome - Obsidev.com
HikaMarket & HikaSerial developer / HikaShop core dev team.
Also helping the HikaShop support team when having some time or couldn't sleep.
By the way, do not send me private message, use the "contact us" form instead.