You have a unit called an FBD, you must use it to repair the rail line you choose. Best strategy is to rail your FBD to Rumania and repair rail from there, it saves a lot of time on rail repair.
Maybe it's not instinctive, but usually, the easiest way to take Kiev is to attack Dnepropetrovsk, once you're there, you can choose a weak spot to cross the Dnepr between the 2 cities, and following that operation, Kiev will naturally fall or the Soviets will risk a big pocket. And make sure you get lots of infantry forward ASAP, panzers do the glamour stuff while the infantry do the punching. The less actual fighting the panzers do, the better, that's a key in this game. And that's even truer for operations against river lines, swamps, fortifications more than level 2, cities and urbans
"The closer you get to the meaning, the sooner you'll know that you're dreamin'" -Dio