Learn English – Should I say “Your order is now complete” or “Your order is now completed”

In computer science, I've heard this called a hop or a segment. In more general English usage, I think the term leg would be most appropriate. As for the whole sequence, route seems fine.

As Kristopher points out, edge is a technical term for what you're describing in graph theory, but an average user would have no idea what that meant. Only use this term if you're explicitly using the language of graph theory.

You should use the verb favourite and not favour. Favour means show an approval or preference for, while favourite means record to enable quick access. It is true that you favourite a video on a website if you like it, but the sense you want to convey here is not that you like the video but that you mark the video in some way. Of course, the past tense of favourite is favourited.