Hello,
I succeed to reproduce nearly every issues on my end and :
1. I used the "Update rates" button of the page "Hikashop->System->Currencies" and the result seems to be better for the UPS shipping method
2. For the FedEx shipping method, is doesn't seem to fully support multi-currencies so we'll work on it to properly enable the support of multi-currency, and get back to you as soon as possible.
3. Regarding the fact that you have to "refresh" before seing your shipping method, we actually fixed it through the next futur Hikashop version that's still in preparation (That's why I wasn't able to reproduce it).
4. For the debug mode, Hikashop is caching every shipping results to optimize your website speed, so the solution can be for example to :
- Try it with your browser private/incognito mode
or
- Update the quantity of one of the products in your cart.
Thank you for your feedback !