Two points:

"..how fast the community has been growing since the beginning. ODER: ...from the beginning ?? ist beides möglich??

from/since its beginnings/its onset would be easier on the ear.
and
ein anderes beispiel: since 2001 she has been working as a teacher. ODER: from 2001 she has been working as a teacher. ?????
'since' in this case. 'From' would ve used with the preterite 'she worked from 1999 to 2001 as a teacher'

,,,,

Your examples are not the same.

"Since 2001" is fine, "from 2001" isn't. But if she has stopped, and you say what she's doing now, then "from". "From 1915 he worked as an engineer." (We know from the context, perhaps, that he died in 1920.)

You wouldn't use "since" with "beginning". I suggest however:
From the outset...
Right from the start...
(You still need a present perfect though, if the time-span continues through to the present.)