1. The arrow has the same color as the line. Use instead bubble layer for the start and end points and set the color there.
2a. The map use to repeat itself (ie US multiple times) but that was consider too confusing, hence the clipping of the world.
2b. Shouldn't be a problem mixing area layers and line layers. however keep track of what should be rendered source and/or destination.
3. Check out the docs for the location service and Michael video: Qlik GeoAnalytics - Troubleshooting a location lookup
4. Check out the "dissolve" operation in the connector, does exactly that.
Overall, using many lines and drill down makes a lot of information, can be confusing to the user. Please use the titles and list boxes to explain what the user is looking at and help him out with the selections.