Driving vehicles on newly poured concrete
Is it really OK to drive on the concrete after only 2 days? No. Even if control joints were cut, the concrete is at a fraction of its ultimate strength (maybe 15-30%, depending on several factors). You run a high risk of breaking it at other locations. 

Will the slab further strengthen by in the order of 25% over the next 12 hours?Maybe, but that's 25% of the current cure extent, which could still be a minor fraction of the ultimate strength. Cure rates depend on many things, from mix to water content to weather to after-pour care. The cure amount does grow substantially over the first few days, but it's folly to take guesses. Give it at least a week (ideally two) if at all possible. 

If I drive over concrete which is still in the early stages of curing/setting and it doesn't visibly crack, am I weakening the eventual strength of the concrete? Cracks due to vehicle traffic are usually apparent right away, but it is possible that you'll crack it and not know it until dirt starts to accumulate on the line or it opens further. If it doesn't crack, it's probably not weakened in any substantial way.

If I drive on the slab prior to joints being cut am I more likely to damage it? No, but it is more likely that you'll end up with crooked (uncontrolled) cracks, which are ugly.

Is the placement of the mesh a concern? Yep. It should've been pulled up into the center third of the slab's thickness as the pour occurred. It's possible that what you see there is an anomaly, but it's not a good sign.