temp's important when its below 40f when the work's best left to pro's,,, above 40, conc can safely be placed, finished, & cured by anyone w/good conc skills/knowledge/experience,,, caution - be certain temp won't drop below 40f & protect conc w/blankets to retain heat generated by curing ( hydration ),,, conc's exothermic yet it needs its created heat to complete the cure.
an overlay's possible using the correct mtls ( polymers, cement, fine aggregate, & water ) but its VERY tricky & i wouldn't suggest the work to anyone inexperienced,,, any jnts/crks present will reflect in the overlay.
1) Will doing a conc o'lay on stone work? possibly yes but, generally, no in your instance.
2) large crks & shallow o'lay? those crks have become working joints & should be addressed w/flexible sealant rather'n any mtl that has no elastomeric quality,,, in short, you cannot address 'em w/conc mix in a bag,,, layering different mix designs will only result in strength to the lever of the weakest mix.
3) see 1st paragraph
4) my best advice ? - post a sign saying ' watch your step '
& replace the stones when the weather's warmer