Use extension API to open links from the popup

Safari doesn't seem to follow links embedded in the popup window (not even
with target="_blank").
Remove unnecessary comments
Set default dimensions for Safari's popup
Use HTML5 download instead of extension API

Benefits:
- Cross browser solution (however only for relatively new browsers)
- Doesn't need extra permission in Chrome

If the browser doesn't suppor the download attribute, then a new tab will
be opened with the exported data.

Other changes:
- Start the download only if the data is not empty (previously the
  download started anyway)
- Reorder code in vapi-client.js for Safari, so unnecessary code doesn't
  run on extension pages