Cool demo. Interesting questions. There are nobel prizes waiting for the answers to some of them.
Warning: The following is not precisely target at your post.
The core of some your questions are the kind answerable only with mu. Essentially, you are asking for some physical intuitions to relate the quantum world up to the world as we see it. But the thing is that there is very little in our macroscopic reality that relates to the quantum world. All analogies are broken. Here's the key thing to realize. Quantum mechanics is hard not because it is complex =). Far from it. It hard because we have no mental basis with which to represent its concepts. The opposite should hold too. A Quantum intuition would find our world bizarre, very hard to understand and - unlike how we feel about QM - justifiably complex. But if one takes a multicultural appreciation approach to how systems evolve, QM becomes a bit less offensive to one's sensibilities.
The only path to approximate intuition is to drill the math and think about the concepts. Simulations are another great option. They allow one to create a rope bridge from the math to something that feels a bit more concrete. Still not intuitive but better than nothing. The idea is to get to the point where you can use the math as a map. So you won't ever be able to feel as comfortable with it as galilean relativity but you can form questions, think about reality and use the map to guide your mind. I am the opposite of you - I think a lot of the physical or incidentals of experiments are useless baggage for building that map.
What does a particle with some particular wave function look like?
At this point it is not useful to think about how things look. Focusing on what things "look" like would again be just be a rough analogy, possibly misleading (similar in spirit to focusing too much on tangent lines for derivatives) and might create a false crutch by waylaying the brain from becoming more comfortable with the abstract surroundings. And then there is the question of: is the wave function? Does it make sense to think of it as something physical? (I don't think so).
Does it occur on scale of nanoseconds? Seconds? Hours?
While kinda opposite in direction to your questions, work on decoherence is answering some questions of timing. But nothing will shed light on entanglement, coherence and aspects of measurements better than quantum computers. Lets hope they get invented soon or less preferably, proven not to be possible. Each would learn us a lot.
Warning: The following is not precisely target at your post.
The core of some your questions are the kind answerable only with mu. Essentially, you are asking for some physical intuitions to relate the quantum world up to the world as we see it. But the thing is that there is very little in our macroscopic reality that relates to the quantum world. All analogies are broken. Here's the key thing to realize. Quantum mechanics is hard not because it is complex =). Far from it. It hard because we have no mental basis with which to represent its concepts. The opposite should hold too. A Quantum intuition would find our world bizarre, very hard to understand and - unlike how we feel about QM - justifiably complex. But if one takes a multicultural appreciation approach to how systems evolve, QM becomes a bit less offensive to one's sensibilities.
The only path to approximate intuition is to drill the math and think about the concepts. Simulations are another great option. They allow one to create a rope bridge from the math to something that feels a bit more concrete. Still not intuitive but better than nothing. The idea is to get to the point where you can use the math as a map. So you won't ever be able to feel as comfortable with it as galilean relativity but you can form questions, think about reality and use the map to guide your mind. I am the opposite of you - I think a lot of the physical or incidentals of experiments are useless baggage for building that map.
What does a particle with some particular wave function look like?
At this point it is not useful to think about how things look. Focusing on what things "look" like would again be just be a rough analogy, possibly misleading (similar in spirit to focusing too much on tangent lines for derivatives) and might create a false crutch by waylaying the brain from becoming more comfortable with the abstract surroundings. And then there is the question of: is the wave function? Does it make sense to think of it as something physical? (I don't think so).
Does it occur on scale of nanoseconds? Seconds? Hours?
While kinda opposite in direction to your questions, work on decoherence is answering some questions of timing. But nothing will shed light on entanglement, coherence and aspects of measurements better than quantum computers. Lets hope they get invented soon or less preferably, proven not to be possible. Each would learn us a lot.