Hi,
1. The system uses the Joomla tooltip system which accept HTML content in the tooltip.
I guess that your template does not use the default tooltip library.
2 & 3. The system uses the Joomla popup system. In your case the popup uses "mootools" but you can configure HikaShop to use the jQuery bootstrap one. Your template is not compatible with the mootools one so it display this strange thing instead.
You can find a lot of threads talking about that (a common error in the Joomla template) where it explain how update your css replacing ".modal" by "div.modal".
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.