1. I tested it using a bigWig and a BED file. Both were loaded nicely in Circos, but I was surprised to see that the visualization of both files looked exactly the same, i.e. both file types seemed to be interpreted as histograms/coverage data. From the Circos plots I've seen in publications, I assumed that BED files should be visualized as straight lines, indicating genome regions (rather than a coverage). Am I doing anything wrong? Or, rather, how should I modify the BED file so that its content is simply interpreted as genomic regions?

This is a limitation of the visualization, and it should be addressed. I've created a Trello card for this enhancement that you follow here: https://trello.com/c/YIdx6QvV

2. In the Galaxy publication (www.biomedcentral.com/1471-2164/14/397), "line data" is mentioned for displaying connecting lines in the center of the circle - could you give me an example line of how this kind of data needs to be formatted?

Score isn't used right now, but it still needs to be there. Once you have this format, you'll need to convert the datatype from 'tabular' to 'chrint' in order to visualize it (click on the pencil icon --> Datatype. Also, I have a workflow up to convert Tophat fusion output data to chrint format here:

Sorry for the cryptic nature of everything right now. We'll get this info and more up on a wiki page eventually (you're welcome to start one in the meantime). Let us know if you have more questions.