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This is largely in the realm of GM call as to what constitutes "interacting with" since only a very exhaustive list of examples were given in the Core book.
There was a 3.5 blog written a long time ago that helped hammer down illusions. Since there is no reason not to believe that would translate just fine to Pathfinder most people tend to use those.
In short, an action must be used to "interact with" an illusion. Whether that action be, speaking with, touching, probing, actively scrutinizing, or anything else. As long as an action is being used that would give the creature any reason to doubt the illusions reality then a save is allowed. If no action is used, however, no save is granted. Simply seeing the illusion is not enough to grant a save.
The exception to this is if the creature is given a good reason not to believe the illusion. Another spellcaster witnessing an illusionist seemingly conjure a massive dragon might realize that such an effect is well beyond the limits of the other mage and be granted an immediate save. Or watching a friend walk through an illusory wall. This part is particularly up to the GM as to what constitutes "good reason not to believe", but a good rule of thumb is anything that would make the character ask "How is that even possible?" (remembering that magic is prevalent, and a 'wall of fire' suddenly springing into existence to not that hard to believe) would do it.
Your examples:
1) No, 100's of feet or 5 feet, distance does not matter. A save will not be granted until the creatures are given a reason to doubt it by taking actions to be granted a save or if the effect is just too impossible to believe. Running behind something and then creating an illusory double of yourself running out the other side is a great tactic because there is no reason for the enemies NOT to believe that and therefore wouldn't be granted saves, right up until they start pelting arrows at it and seeing them go right through 'you'. Then they would be granted a save, failure means they still believe the illusion and just assume they must be missing you.
2) Same deal, no one in the crowd just passing by would not be given a saving throw. However, the gate guard asking you for your identification would gain a save because he's directly interacted with you and your illusion. Or the spy tasked with specifically looking for you and forewarned you might use illusion to mask yourself, might spend his actions staring at a crowd trying to see past illusions would also be granted a save because he is spending actions to actively scrutinize.