Minor illusion:
You create a sound or an image of an object within range that lasts for the duration. The illusion also ends if you dismiss it as an action or cast this spell again.
If you create a sound, its volume can range from a whisper to a scream. It can be your voice, someone else’s voice, a lion’s roar, a beating of drums, or any other sound you choose. The sound continues unabated throughout the duration, or you can make discrete sounds at different times before the spell ends.
If you create an image of an object–such as a chair, muddy footprints, or a small chest–it must be no larger than a 5-foot cube. The image can’t create sound, light, smell, or any other sensory effect. Physical interaction with the image reveals it to be an illusion, because things can pass through it.
If a creature uses its action to examine the sound or image, the creature can determine that it is an illusion with a successful Intelligence (Investigation) check against your spell save DC. If a creature discerns the illusion for what it is, the illusion becomes faint to the creature.
-Physical interaction with the image reveals it to be an illusion.
Not an action spent physically interacting, but physical interaction. An arrow strikes the image? Revealed to observers. You use an object interaction to touch the illusion? Revealed to observers.
-If a creature uses its action to examine the sound or image, the creature can determine that it is an illusion with a successful Intelligence (Investigation) check against your spell save DC.
If, not only if. This could reveal the illusion without physical interaction, and is particularly useful if the illusion was behind a window of out of range.
Indeed. And in fact it works with illusion spells of lvl 1 to 3 too.
But metagame can severely limit the efficacy of the spell. IMO the two rules are there to fix the metagaming around the spell: either you spend an action to see through the illusion, or you use an attack. In some situation, a free interaction can be legitimate, but in case of disagreement, I would fall back on one of the two rules.