If you are new to Spanish, you shouldn't be troubling yourself to understand what you think to be anomalies. Each of those words/phrases has it's own purpose in the language, it's not like you just pick one and use it.
Yes, they all mean
from. But even in English, there are different variations of
Since, Starting at, Originating, Deriving, Materializing, Dematerializing
Desde is used to introduce, indicate and designate a starting point in your sentence, and always in the past.
Desde el día que llegué aquí comía muchos legumbres.
Since the day I arrived here I ate a lot of vegetables.
Mi padre me dió una cerveza cuándo era niño y desde entonces yo era alcohólico.
My dad gave me a beer when I was a child and since then I have been an alcoholic.
A partir de does the same thing but it's more flexible. This preposition allow you to set your starting point in the future.
A partir de la próxima semana empezaré a hacer ejercicio.
Starting next week I will start exercising.
A partir de que llegue Pablo prepararé la cena.
As soon as Pablo arrives, I will prepare dinner.
Se explotará una burbuja a partir de que se la toque.
A bubble will explode as soon as it is touched.