Question 1: on the CRT on a DS result German and Fascist units after being shattered are returned to the cup. This is, I suppose, only valid for round units with the 3 cups.
Yes this is what the rules say.44.7.1:
Eliminated Fascist Italian and German Kampfgruppe round units and Fort hex-shaped markers are placed back in their respective draw cups when eliminated. They are never put in the Surrendered Units Box.
Question 2: Card 10; German player hands over card to Allied player on turns with a death head. On no such turns nothing happens. Which player must roll a die to gain or loose an Event VP? Does this happen on all turns or only on death heads turns?
The German must follow the black instructions, then gives the card to the Allied player.
So the Germans rolls the dice and can Gain/Lose the Event VP. This works on all turns.
BUT the Leader check is only done during death's head turns, as per rule 5.6
Question 3: During a major invasion 2 landing zones with bordering LZ-hexes may be chosen, while US and CW units must be evenly selected. Can US units and CW units land on any LZ-hex or each only in ONE same zone, so the US lands in one zone and the CW in another. How can this be managed if one zone contains only 2 LZ-hexes, like west of Palermo and the other say 5 like south of Gela or southeast of Syracuse? Note that according the rules on the South Italy map there are 2 landing zones on the Toe not one!
There is nothing in the rules that forces the Allied player to segregate the Landing Zones, so you can mix-and-match as you wish, but note rule 14.6.10
Question 4: when and how (which rules?) can the German unit (or their Italian friends) leave their cups to enter any Shattered or Reserve box and renter the map again?
They can't unless they enter by Game Event play (ex: the Italian Armistice Table), card play, or KG breakdown.
What is the reason of German units putting in a cup over sending them like the Allies to the shattered box?
ONLY the round Kampfgruppe, Italians and the forts go into a draw cup (as they are randomly drawn when replaced!).Not all German units.
Question 5: there are a limited number of reserve markers. If cities are taken and all reserve markers are in play but not used, is the extra bonus for taking the cities then waisted? This involves some planning to buy extra cards before cities are attacked and taken....
Yes this is correct. Your Supreme HQ decides that you already have way more resources available to use and sent the extra to other fonts. So the points are lost.
Question 6: if weather is fair and an Allied mech unit rolls a red result it could move 2 hexes instead of a possible 3 to make a second attack. The 2nd hex entered must not be a TEC hex halting further advance to be able to make a second attack, but must be the 3rd hex the hex of the defender or any other hex to keep the 2nd attack possibility?
You may attack any other hex, you are not limited by the hex of the regular combat defender.