1) Example, Kharkov is Soviet controlled (but no unit in it), and the area surrounding is out of supply. May the Soviets place a new unit in Kharkov then.
You can only place a unit in a hex if you can trace supply to a city (rule 7.6). The city itself is not a supply source. I suppose here that the city is surrounded by enemy units and ZOCs, if this is the case then you cannot trace supply to it, and cannot place a new unit there.
2) The first turns the Soviets may not stack, may they overstack when placing units?
Sure you may overstack, but rule 8.4.3 means that the overstacked units will be immediately placed in the Shattered units box at the end of the Organization Phase!
[8.4.3] Overstacking Penalty: At the end of any Phase or Battle, the owning player must put any excess units of his choice from that hex into the Shattered Units Box until it conforms to the stacking limit (8.4.1), Unsupplied or Fortified units are put in the Destroyed Units Box.