Chris covered quite a few things so I'll give these a try. Let me know if I missed any.
The biggest question surrounding the Spider Clan, to me, is: What is the Spider Clan's agenda?
I'd say the real answer is that the agenda has changed several times over the years, depending on Kanpeki's plans. The latest blow was, of course, Seiken being chosen as the Heir. More direction will soon become apparent - we're working on a 20 Festivals fiction which will show the state of the Clans as the story begins, and Spider will be in part 1 (We're spoiling you guys!)
I know this doesn't really help, but between the time jump, the team changes and several editions, it's no surprise the Spider has been fluctuating. But we hope to consolidate the identity of the Clan going forward.
Also, Daigotsu is some poser? Really?
What is the role of the Goju and Ninube within the Spider (allies, infiltrators)?
This will somewhat be addressed in 20F part 1. I've made it a personal task to make the Goju and Ninube more regular features!
What is the role of re-emerged clan-aligned Shadowlands Horde?
The what now? What are you referring to?
This is a good example of something which might be clear for you, but not so much for us or everyone. Make sure we know what you're referring to, folks!
What is the Spider Clan best at?
That's a dangerous question, in that while Clans generally have fortes, they're never absolute. Otherwise, Crane being the best at dueling, they would win every Emerald Championship, yet they do not. The same way Lion are the best tacticians, yet lose battles. Also, no Clan is one dimensional - you could say the Crab are the best at siege warfare, but that really doesn't apply to the Yasuki, for example. But overall, I would fall back on the common theme of the Spider as I see it, which is power. Acquiring power and ruthlessly exerting it - that's the Spider way. Their lack of concern for others, even including their own, makes them dangerous.
What is the role of the Spider Clan as a whole?
That's kind of the same as their agenda. Officially I'd say they're still seen as the conquerors of the Colonies, although they're more of an occupation force than a conquering one right now.
Hope this helps!