Install latest CB, install latest CB Core Fields Ajax. Next edit the Canvas field and under Integrations > CB Core Fields Ajax set "Profile View" to "Enabled" and "Profile View Output" to "Tooltip". Canvas field can now ajax edit fine. Do the same for Avatar and it too will work fine. No additional changes needed. Yes, the CSS still need some improvements, but progress has been made already. Below are the feature tickets where I noted this still needs some better UX improvements.

forge.joomlapolis.com/issues/6061
forge.joomlapolis.com/issues/6062

Development has only been slow due to 4 months working on our new site. My blog was to to show things are back on track. Can't exactly fault us for wanting to use our own product (CB 2.x) and getting away from Joomla 1.5. We're using several of our plugins on JP now actually.

The alternative for me is to move to one of your competitors but I'm keen to avoid this as I've spent a lot of time and energy and money working to get CB working for my site (no doubt a bunch of your other customers have already done so).

I can't stop you from "jumping ship" as that's your choice. Neither has remotely close to a robust gallery that CB Gallery is about to provide. CB Activity provides customized activity streams and an API to output them (you can have an activity stream for whatever you want). None of them offers anything even remotely close to CB Auto Actions. Any field can be ajax edited using CB Core Fields Ajax. CB is entirely modular. Use what you need only. This avoids bloat for simple sites and complexity for sites that need it. Your statement regarding a bunch of other customers is beyond false; we've had significant growth actually.

My current development pipeline is planned as follows.

CB Gallery > CB 2.1 (backend UI for language overrides and more!) > CB Activity > CB Privacy

Both CB Activity and CB Privacy will receive large API improvements as well as significant improvements to their usages. Streams will become more robust and finally have the proper API to be extended by say CB Gallery for uploading from a stream.

After the above I'll be cycling through other plugins like CB Core Fields Ajax and clear their tickets. Once that's done I'm going to start some new projects.

1. Just tried to do this and found that it seemed to work somewhat when I deleted the online indicator using Chrome's web Inspect. What's the correct and easiest way to disable this? I couldn't find any plugin.

You don't need to remove the online status field. Please read my reply above. Update CB to latest build then update CB Core Fields Ajax to latest build and configure the fields ajax usage as instructed above.

2. To confirm - do I need to also make the css changes in the other thread (linked to above)?
As mentioned, I tried this before and found that when the user tried to edit their profile on mobile, the drop down menu was blocked by the Avatar pic..

No, you only need to update and configure it.