Not really. Cyanogen is OK, but it's just Android. The hardware problems are still there: i) no drivers so GNU/Linux can't be ported ii) the baseband processor is usually badly isolated so it's easy to attack the device.
You do, this is Ubuntu Mobile strategy at the moment AFAIK.
However, drivers in ARM platforms are very opaque. You rely upon the goodwill of the manufacturer to update them, and most of the time they don't. See how most devices get unsupported in Cyanogenmod after a while.
And in any case, all the privacy concerns remain. It's a hardware issue. Android would be fine.
Not unless you use a popular phone model since each phone needs to be individually ported. I just bought a Mi Note (http://s1.mi.com/m/product/minote/index.html) and am out of luck.
For now you can install arbitrary custom Android builds on a few commercial devices until all the device bootloaders have Trusted Execution Environment (TEE) signing schemes preventing any user changes. Mobile devices are becoming increasingly more tightly sealed blackboxes not more open.