That material is quite a bit older, but that's when I was focusing more on (3), so hopefully it clarifies things.
The main idea though is: when you're inventing a new algorithm to do something, you're typically thinking in terms of operations on data structures, rather than something lower level like lines of code in a particular language. So, if you use this tool while attempting to write your new algorithm, it will give you a visualization of what your code is actually doing to the data structures involved, versus what you thought it was doing.
That material is quite a bit older, but that's when I was focusing more on (3), so hopefully it clarifies things.
The main idea though is: when you're inventing a new algorithm to do something, you're typically thinking in terms of operations on data structures, rather than something lower level like lines of code in a particular language. So, if you use this tool while attempting to write your new algorithm, it will give you a visualization of what your code is actually doing to the data structures involved, versus what you thought it was doing.