Hi Anders,
Yes currently there is a know limitation that Data Workbench works fine only on Chrome but this is being worked on will be fixed for other browsers. Regarding the issue with Lead template download your understanding is correct that you can download an empty template file from the Download CSV file for Object link. I just tried the same and was able to download the CSV template which has all the fields and attached is the downloaded file. Also there are few workarounds to keep moving instead of waiting to get this template issue resolved you can create your own CSV file with the columns you wanted then you will be allowed to map those fields on the subsequent screen. Another option is select Lead object move on to next screen and upload any CSV file you may have then the mapping screen will reveal all the fields that are part of the Lead object. Hope this helps.
Can you please elaborate on the issue with Business System could not be found? If you still face any issue please report an incident on component LOD-CRM-INT-DWB
Thanks,
Prakash