The question I have, what happens when the Sauron player initiates a siege fight (I'm probably translating this wrong, the Dutch term is 'belegeringsgevecht', the besiegers attack the stronghold). Is this counted as an attack and should Gondor move to 'in war' on the Political table or not?
That is correct.
The second question pertains the "Blade of Westernesse" action card that can be used in combat. If a Hobbit is present, a hit on a leader roll can kill a vassal of Sauron. The card doesn't specify the vassal has to be present in the battle so it could be any vassal on the board. It seems illogical to me though. How can a Hobbit, fighting in Mount Gundabad, kill Saruman who is in Orthanc? Yet according to the card this should be possible. Is this possible?
No. Combat card can only afftect units, leaders and/or Minions that participate in the battle. Per the rules:
It is not necessary to attack with all units of an Army; it is possible to commit only a portion of the Army to the upcoming battle.The remaining Army units (and Leaders/Characters) are considered to have been left as a rearguard, do not participate in the battle, and cannot be targeted by combat cards, chosen as casualties, or chosen to advance into the contested Region if the battle is won.
The last question pertains to leadership and Gandalf the White's ability to neutralize leadership of Nazgul in a battle. Some Dark action cards have a pre-requisite, namely that the total leadership of Nazgul should be higher than the total leadership of the Light army. Does Gandalf's ability completely ignore leadership, making such impossible to play or does it only kill the leader-rolls?
Gandalf's ability is that he negates the leadership of all Nazgul in the battle at the forfeiture of his own. Therefore if he choses to use that ability all Nazgul in the battle are considered to have a leadership of zero for all purposes.