The ALLOY OF LAW symbols are not a different alphabet from the one used in MISTBORN 1. It is just a more modern font. (In-world, there would be a variety of fonts, as there are in our world.] The traditional font is still legible to the majority of the population, and is still used when they want an old-fashioned look.
Moving the dot to distinguish vowels is a modern innovation, within the last 100 years by ALLOY OF LAW. I suspect that dots may be gone entirely (except for the two changed vowels, and maybe "capital" letters) in many fonts by the time you get to the second trilogy. Numbers might get a moved dot too. The placement of the dots in the original symbology has to do with Allomancy, but they're largely superfluous in writing.
The Feruchemical symbols (which are in the RPG) are evolved from the same root (the ancient symbols you can see in MISTBORN 3), but I don't know about their use in modern writing. It could be something like the hiragana/katakana distinction. But that's just speculation right now.