'Ship Transport' can only be used for Marching and Retreating
This means that, in your eample below, units at sunspear cannot Support the battle at winterfell.
This also means that, if the units at sunspear had been given a Raid order, they could not have Raided winterfell.
For the question of Tides of Battle Skulls, the rules don't say it exactly, but I would use the same principle as casualties from Sword icons. Casualties from Sword icons are only taken from the units that were defeated in combat and have been forced to retreat, not from Supporting units.
For example, I get attacked by the Lannister player and I only have a single footman at that location, but I have two additional footmen with a Support icon nearby, so they add their support. The Lannister player uses the Gregor Clegane house card and I play a weak card with no Fortification icons. I am defeated. As the Gregor Clegane card has three(!) sword icons I take three casualties from my retreating units. As I only have one retreating unit it is removed. I do not also remove the two supporting footmen. Gregor's extra two swords have been wasted.
I would apply the same logic and say that skull icons can only cause a casualty from the units (attacking or defending) that are actually present in the battle, not suporting units. If there are no unts left to remove, the skull icon is wasted. This could happen because, for example, Mace Tyrell was used and removed the only unit that the opponent had before the skull can come into effect. T