Hi,
Do you have the issue with a coupon in the cart with the plugin deactivated ?
If the emails are in the email history, then HikaShop did send the emails to the email server of your hosting. So either they got blocked by the email server of your hosting, or they got blocked by the email server of the recipient. And supposing that you have the issue with a coupon in the cart with the plugin deactivated, the reason could be the fact that there is a coupon code mentioned in the email, which would lead the email server to flagging the email as spam and rejecting them.
Regarding the orders with a 100% discount, you should activate the "validate free orders" plugin in the Joomla configuration and configure it to change the status of the order appropriately. Also, you can add a "text" block to your checkout workflow with a hkshow tag:
www.hikashop.com/home/blog/471-hikashop-4-4-3.html#tags
For example:
{hkshow maxcart=0.001}Please click on the finish button to validate.{/hkshow}
Or you could try:
{hkshow maxcart=0.001}<script>document.getElementById('hikabtn_checkout_next').click();</script>{/hkshow}
which should auto validate the step (never tested yet).