I don't understand the problem.
First, a character is not flat-footed outside of combat. Flat-footed is defined in terms of being in combat, i.e., in initiative. No combat, no initiative, no flat-footed. It's irrelevant that feather fall is an immediate action, outside of combat, just as it's irrelevant that stone shape is a standard action, outside of combat. Outside of combat, feather fall is just a spell you cast to slow a fall.
I don't think so.
What is your AC outside of combat?
Do you have full AC and all of Dex bonus to it up until you roll for initiative and then suddenly lose it until your turn in the initiative order?
I do think that turns and rounds do not exist outside of combat though.
It has to be understood that the D&D combat system is very vague in its design and so it doesn't always make sense or follow a totally "logical" path.
Second, if you are in combat and flat-footed, I don't understand why it's so unthinkable that someone deliberately trying to make a wizard's teammate fall might actually succeed in doing so. Why is it so difficult to believe that a wizard could be caught gawking by the sudden eruption of combat?
This I agree with this totally.