Your expert in all things ratings. :)
From the standpoint it's the oldest of the DC series', then yes Arrow could be the first to go. Don't base that off of just last week, though. The series has been a consistent 0.5 for the season, it's in no danger of cancellation for this year at least. :)
The rumor on Agents of SHIELD at the end of last year was that ABC wanted to cancel it and Disney nixed the idea as they still had tie-in plans with the MCU universe. Not sure how true that is/was, but I hope they got everything done they wanted because there is no way ABC is gonna renew it with the numbers its put up so far.
Supergirl ... yeah I don't see the appeal honestly. Now granted, the only episodes I've seen are ones that cross over with Flash (or Arrow and Legends) but the writing seemed shallow and the acting was terrible. If the point of crossing over all the shows is to get cross pollination of fans watching all of them, it's been an epic fail for me at least. I don't know enough about the DC comic-verse, would Black Lightning get pulled into the cross-over madness next season?
@gmpugs, This isn't even the lowest rating for the season, so my guess would be the holiday played a role as least somewhat. I haven't watched any of this season yet (or last season now that I think about it) but the ratings have been in the 1.0 - 0.9 range for the most part. It will be interesting to see what happens with the numbers for the cross-over. Will it pull up Arrow and Legends a bit or pull down Flash and Supergirl?
Not booted, but certainly delayed. The CW hasn't said when it will be back; I'd expect it sometime around March. There will also be Olympics coverage to deal with, so I'm not sure if any network will run original programming against it. Legends is in no danger, it just needs to wait for a hole in the schedule.