I’ve been working through doing this for each class as a stupid ‘complete before Pre-Patch’ challenge, and can confirm that both these steps are still active.
Legion invasion timer can be found through Google (unfortunately I’m not trusted enough to post a link ) which will tell you when the next invasion is happing - at time of posting, one should trigger in about 2hrs 35mins.
The Champion quest you should be able to pick up from your Order Hall once you’ve completed both the class campaign and the relevant steps of the Broken Shore questline - one thing I’ve tripped over a couple of times is not completing the weapon upgrade quest after the one which rewards your Order-Specific title, which you need to do.
Edit: (or why Yas shouldn’t post pre-caffeine)
Championing Our Cause is the ‘complete a Legionfall mission at your Order Table’ one, not the recruit a Champion (oops!). That mostly just relies on you having a mission with the location Broken Shore, sending Champions and successfully completing it. Sorry for any confusion!