1) I have The Strain paused at home. When I walk in the door, I'll tap the button and resume watching it.
Right now Cortana doesn't know about this, but Xbox Video does and you can pick them up on your phone, PC or Xbox.
2) I have Pendulum - Midnight Runner paused on my HK BT headphones.
Cortana can play music for you via voice commands. Finding out what's currently playing is visible in a number of places on the phone already, I'd rather not have it show up in Cortana's feed as well (and I haven't tested if it does).
3) It's going to rain a lot this week
Cortana shows me the weather in its feed and gives automated weather alerts for serious events
4) Google stock is doing really well
Cortana also shows stock prices for companies. I have it showing me the stock of the company I work for.
5) It's Jen's birthday in a week. Thank God it reminded me. I had forgotten.
Calendar entries show up with Cortana as well. I'm pretty sure birthdays show up as part of that, including those from FB if you've connected that up to your Calendar. They might also show up in the Notification Centre from the FB app. Cortana can also let you add a reminder to say happy birthday to Jen the next time you talk to her.
6) Four people added me on G+
7) Mike Elgan just retweeted one of my tweets.
So there's limited Google services on WP (talk to Google about it) but in a similar way this kind of thing shows up the Notification Centre from the FB or Twitter apps and I'd rather it there than in my Cortana feed. I know Cortana has app integration though so I imagine the cross sharing will only increase over time.
8) My favorite food truck is still outside
Depending where you got this from (i.e. FB/Twitter, an app, something built in to Google Now) you could get similar notifications through the WP Notification Centre. As I said Cortana gives restaurant/food & event recommendations for things local but I can't say it's hooked in to that food truck specifically, we'll assume not.
9) My Eve Online character is about to fall out of training.
Again something I'd expect to see in the Notification Centre rather than Cortana's feed. But as Cortana has open APIs this could also be possible for the future.
10) My first meeting is at 8AM tomorrow
Cortana does this.
11) dum waldo just commented on my post about how Xiaomi just obliterated Apple and Samsung in China.
12) I have 3 work email, and someone just tried to ninjavite me to a meeting, and I declined.
Notification Centre, which makes sense to me.
It all just worked perfectly without me having to engage Google Now to feed it any of the above.
I would assume that for anything that uses an account, i.e. Google+, FB, Twitter, Eve Online, meeting requests, etc., you would have had to give Google Now access to these at some point, and if not then I'd be very worried. The same thing needs to happen on WP and with Cortana and a lot of Cortana integration with these services comes from the integration with third party apps, so this will improve as revs update their apps.
What I'm trying to say is that you wrote off Cortana as needing interaction to do anything, that's not true. I think Cortana is just as intelligent behind the scenes as Google Now, but there are obviously still some gaps in the kinds of services that Cortana is hooked into and this gap will decrease over time as MS and third party app devs add more functionality.
As I said before, I was very impressed with Google Now when I saw it recently and it seems like it still has the upper hand in volume of stuff it knows about, but underneath I think Google Now and Cortana are very similar things in that respect.