Isotop

You are wrong. "Within 6 inches" includes "6 inches away". Here is the relevant part from the Core Rules:
 
"[...]So, for example, a unit is within 12" of another unit as long as any model from one unit is 12" or less from any model from the other unit[...]"
(https://www.games-workshop.com/resources/PDF/AoS_Rulesheets/ENG_AoSSW_Rules_booklet_web.pdf, page 2)
 
You are absolutely right about this. Even without the actual rules at hand, you provided an intuitive and elegant explanation to the problem. Another person voting you down without even discussing your argument shows that you left no real room for a counter argument. 
 
Your intuition is correct. If an "Ambush" ability states that the unit has to be wholly within 6 inches of the battlefield edge, the following Designers' Commentary clarifies the meaning of it:
 
"[...]A: A model is wholly within a certain distance if every part of its base is within the stated distance[...]"
(https://www.warhammer-community.com/wp-content/uploads/2019/07/8f9bd00c.pdf, page 3)
 
In combination with the quotation about "within" above we can see that "wholly within 6 inches of the battlefield edge" means that one point of the models circular base can be exactly 6 inches away from the battlefield edge. Lets put the model on a line with the objective and let the line be perpendicular to the battlefield edge. Since in your example the center of the objective is 12 inches away from the battlefield edge, it means that it is now exatly 6 inches away from the "6 inch point" of the models base we discussed beforehand. Since "exaclty 6 inches away" is included in "within 6 inches", the model is now within "capturing distance" of the objective.
I am sorry that multiple people were trying to tell you that you are wrong and did so without any backup from the rules. We should always be wary when people speak from intuition alone and fail or not even try to connect their statement with the actual rules of the game.
I hope my explanation is clear and that you can make use of this knowledge during your future games.

There is no such thing as a "deployment zone". Each Battleplan has defined territories for each player and further clarifies in which manner armies are deployed in them.
I hope this clears things up for you

Running only prevents the unit from shooting later in the same turn. Therefore it will be eligible to shoot in the subsequent opponents turn.
About Steady Aim: I am not a native english speaker but I can not imagine what "preceding movement phase" could mean other than "the last movement phase" (in your opponents turn).

It does not stack, since Arcane has an "any"-wording:
 
"Arcane: Add 1 to casting or unbinding rolls for Wizards while they are within 1" of any Arcane terrain features."
(https://www.games-workshop.com/resources/PDF/AoS_Rulesheets/ENG_AoSSW_Rules_booklet_web.pdf, page 10)
 
Further explanation of the usage of "any":
 
"Q: When the word ‘any’ is used in the criteria for an ability, how many times is that ability applied when the criteria for the ability are fulfilled? For example, if an ability said ‘Add 1 to hit rolls for models that are within 6" of any models with this ability’, would I add 1 to the hit rolls of a model that was within 6" of three models with the ability, or would I add 3 to the hit rolls? A: The word ‘any’ is treated as being synonymous with ‘one or more’. In your example, this means that 1 would be added to the hit rolls, not 3.
(https://www.warhammer-community.com/wp-content/uploads/2019/03/age_of_sigmar_core_rules_designers_commentary_en.pdf, page 7)

Correct:
 
"Q: Sometimes a spell will have an area of effect (e.g. all models from a unit that are within 18" of the caster, or all models within 3" of a point on the battlefield that is within 24" of the caster). If an ability increases the range of the spell, is the size of this area of effect increased by the same amount as the range is increased? A: If the area of effect is measured from the caster, yes. If the area of effect is measured from a point on the battlefield, no – the ability will increase the range to the point on the battlefield instead. To carry on your example, if an ability increased the range of a spell by 6", then in the first case the spell would affect all the models from the unit that were within 24" of the caster instead of 18", while in the second case the range of the point on the battlefield would be 30" instead of 24" but the spell would still only affect models within 3" of that point. Note that if area of effect is measured from a point on the battlefield, and that point is ‘anywhere on the battlefield’, then an ability that increases the range will have no effect on that spell."
(https://www.warhammer-community.com/wp-content/uploads/2019/03/age_of_sigmar_core_rules_designers_commentary_en.pdf, page 3)
 
Since the area of effect is measured from the caster, you are good to go @Dreadmund.

I agree with you and it is right here in the core rules:
 
"When measuring distances to and from objectives, always measure to and from the centre of the marker."
(https://www.games-workshop.com/resources/PDF/AoS_Rulesheets/ENG_AoSSW_Rules_booklet_web.pdf, page 11)
 
The objective itself is a single point located upon the plane of the battlefield. The "scoring area" (I think that is what you mean @Vextol?) is the set of all the  points with a distance of 6" or less from the objective. Reading this sentence again, we should probably call it the "scoring space" instead.

"Named characters such as Nagash, Archaon and Alarielle are singular and mighty warriors, with their own personalities and artefacts of power. As such, these models cannot have a command trait or artefact of power."
(https://ageofsigmar.com/wp-content/uploads/sites/12/2018/06/AoS_Rules-ENG.pdf, page 17)
It does not talk about traits in general, but command traits specifically. Unless we are missing something, @Bradipo322 is correct (RAW).