Hi,
For the auto reload, it's the calendar system of Joomla which doesn't handle the onchange event properly. It should trigger it only when changing the selection and not just when choosing another month since the selection is not finished.
The only solution to avoid that would be to not auto reload at all and have a button next to the fields but it's kind of lame. Embedding our own calendar system just for that is not an option.
I'm not sure what we should do yet. If you have suggestions on the user experience on that I'm happy to hear them.
Regarding the data that goes one day before, that's because of the timezone handling which is not done for these fields.
The difference between your two websites is that you have configured a timezone for one and not for the other or something like that.
That will be fixed for next version of HikaShop to be released soon (in a week or so).
And the export without selection will also be fixed for next version.