I think I've managed to confuse myself about this too now lol - its been a while (plus the math works out so its easy to just not think too hard about it 😅)

I'm sure I've butchered this! But here's maybe some nice references :
https://www.youtube.com/watch?v=A9tKncAdlHQ
followed by
https://physics.stackexchange.com/questions/46237/is-the-wave-particle-duality-a-real-duality

actually I should be more clear here 😅 probability of getting atleast 1 head can be summed from probabilities of getting exactly 1, exactly 2 etc. Waves on the other hand are fuzzier because if you don't restrict it spatially you aren't summing up from discrete localized coins, there's a "coin wave"

that's definitely one way to do it, atleast bounding it spatially. I think its a bit like a counting game. if you flip N coins and count how many heads there are, you always get a particle like answer, i.e the probabilities for each number can be added.

your intuition is correct! particles are ~waves of definite momentum and mass (which are defined concretely). if you have a free particle that just behaves like an unlocalized wave. but if you put it in a different environment (squished inside bounding box for eg) it becomes more particle-y