Does anyone know how to make new tags with custom colours?
It is clear how to change colours to a predefined set of available colours, but I have no idea how to change to a custom colour. (With the colour picker? Changing templates?)
The seven colours are unchangeable, because this is needed to provide backwards compatibility with earlier versions of OS X (where they were called labels, you could only have one, and you couldn't change the colour).
If you want a detailed explanation of why tags were implemented this way, and why that restricts the tag colours to the default, then I suggest reading page 9 of John Siracusa’s Mavericks review.