I don't have a Hacker News account, so I cannot post it there myself. In the past, others have posted my previous blog posts on HN and they didn't get much response, so I don't think this one would be any different.
In any case, I already wrote a blog post about this: Heat Maps Revisited, and a previous one explains the UI changes in a bit more detail: Interactive Heat Maps.
Not sure if you are actually interested in the questions you asked or just showed them as examples, but I will try to answer them briefly:
This was a huge time sink, as I experimented with a lot of options and I'm still not completely happy with the result. Currently, the color scheme uses a magenta base with linear luminance changes (it is magenta, because this color does not appear to be used on the map itself). The colors are allocated according to the number of data points in each dot.
I already had a package for this, written several years ago, map-widget
Something more interesting: Home · alex-hhh/geoid Wiki · GitHub, which is a Racket implementation of this idea: https://s2geometry.io/. This library is the difference between being able to show interactively ~200k points in the first version and being able to draw 4.36 million in the current version (which is all the GPS points I have in my database, including running , cycling, etc)
Dots represent a small area (small relative to the zoom level of the map) around them and all GPS points in that area are grouped inside the dot. Color of the dot changes with the number of points inside it.
Each point is drawn independently of all the others, so there are no intersections, unless you mean something else?
The visualization shows the data that was collected by the user. To give an example, if you ride your bike on a road in 2020 and the council tears down the road in 2021 to build a park, the fact that you rode the bike there in 2020 does not change and will be shown on the map, which might show a park there.
As for "GPS glitches", they are shown too, as the application displays the data that the user has. The glitches could be corrected, but I didn't have too many problems in my own data, so I didn't implement such a correction. Interestingly, elevation data is more prone to errors and I do have a correction algorithm for that.