I'm not exactly clear on the difference between "time" and "timing"...? Like an accurate incrementing time offset from some unknown start point?

I assume they are referring to the channel timing? Cellular frequencies are segmented into time segments where each channel is allowed to be used by only some devices when it is their "turn" to transmit (this allows multiple phones to share the same frequency at the same time).

Timing is all about periodicity; if something beeps every second, you can measure intervals between two beeps but have no other information. It's often the case that timing is also synchronized to, say, second boundaries too, and most time sources would do this. Time would then be giving some indices to those beeps; the time source would beep and say that it was the N-th beep so that you can work the actual time out from N.

How can you access this timing I run a little mobile proxy service for myself and a few others, could add some value there. Mobile networks are quite interesting.

Is there any difference between a phone with no sim, and a phone with an old sim that's not linked to an active account?