Hi,
There is no options to display the price with discount in these places.
So it will require some modifications.
For the checkout, you want to go in the Display>Views menu and edit the show_block_cart view file.
There, you can add such code at the top and it should do it:
<?php $this->params->set('show_discount', 2); ?>
For the emails, you want to edit them via the menu System>Emails. There, you can add the tag {LINEVAR:PRODUCT_PRICE_BEFORE_DISCOUNT} to add the price before discount, for example, after the tag for the price after discount: {LINEVAR:PRODUCT_PRICE}
Since you didn't provider your version of HikaShop in your message, note that this tag was not available several years ago. So if you have a really old override of the preload of your email, or a really old version of HikaShop, this won't be possible.