Just a couple of thoughts...
Utility of Action Center- probably worth noting that Windows 10 is already slated to expand the number of quick actions (in addition to actionable notifications as you mentioned).
Camera App- I would like to see a few additions but I disagree about the “major overhaul”. The Nokia Pro Cam app was arguably one of the best shooting apps with its brilliant manual mode that you could easily get into and out of. Then to be fair, Lumia Camera 5 itself was close to a major overhaul that offered some dramatic improvements:
- The shooting experience is now much, much faster
- Moment Capture so you can pull individual frames from video, which on the 930 or 1520 means an 8MP still image from a 4K video clip; this is not nearly as easy on iOS or Android
- Rich Capture, which handles not only traditional HDR but also a unique way to turn up/down the amount of flash in flash-assisted shots. I prefer having this as a one-tap button right on-screen rather than having HDR be the default for every single shot
- Living Images (though I wish they could figure out a way to make these work on the wider web)
- Improved manual controls like Exposure and focus for video
That said, there are definitely some things I’d like to see in the camera. Slow Motion video and a better Panorama experience top the list. And I agree that there are too many Microsoft/Lumia lenses, some of which should be baked into Lumia Camera. Maybe add another radial dial for additional modes (as an aside, I really do not like the way the iOS camera app handles the mode switching- too many things to cycle through; they need to break those out somehow). Maybe a radial dial for Lenses (or modes) that you can select from without actually leaving the main camera app.
As far as accessing the camera, many Windows Phones already have a dedicated camera button; you can also put Camera in the quick actions for easy access from the lockscreen, Start or any app.
In regards to Cortana, certainly expect Cortana to continue adding context-sensitive alerts and capabilities; but I’m not sure about changing what the button press does by default. Your suggestion of directly launching Cortana into more app-specific contexts is interesting and has merit. I would point out however, that in both Windows and Windows Phone there is already precedent for users rejecting “context-sensitivity” in favor of “consistency”. Microsoft actually set up Search to be context-sensitive several years ago but had to backtrack when too many people found it unhelpful and/or baffling; users wanted consistency. Maybe Cortana could be different, but I’m not confident. Perhaps they could use the first “card” area to show app-specific stuff, then scrolling down would lead you to your interests. If they hadn’t so obviously deprecated Pivot controls, that would have been another route. Just as a Bing search has different pivots for web, local, images, videos, news, phone they could have put pivots into Cortana for different functions (e.g. scheduling, travel, interests, app controls, etc.).
3rd party keyboards? Meh,,, maybe? The current WP keyboard is pretty darn good. You can instantly switch from tapping to swiping and it has fantastic auto-correction and auto-completion. Not sure how much more you need for “parity” with iOS and Android. iOS actually limits where and how you can use 3rd party keyboards so you’re forced to switch back to the stock iOS keyboard (which I’m sorry to say is absolutely a step below WP or Android).