I wonder if there are any legal issues if I took the description
of the api and implemented my only library, which would be for
my purposes a sufficient replacement.
"Clean room" reimplementation is legally safe (in most countries,
anyway). For instance, if you take a free program designed to use the
library (but which doesn't copy anything from the library), rediscover
the library's API by looking at the calls made by the free program, and
reimplement the library from that, you're definitely safe. You're safe
looking at the published documentation of the library as well, as long
as you don't copy literally from it.
Interfaces themselves can't be copyrighted; only texts can be
copyrighted. Referencing published works for information is legal as
long as you don't copy any text (or only copy uncopyrightable segments
of text). (Because the information is published, it can't be trade
secrets.) Patents are another matter entirely, but it's best not to
think too hard about them. :-/
Couldn't I publish my
code without running into problems? May a use the header files
from the commercial library or at least to the user of my
library where to get them?
You can use *uncopyrightable* portions of the header files. It might be
legally safer not to mess around with the header files, if you can
easily reconstruct appropriate "work-alike" headers from safer sources.
(After all, your library needs its own headers, and you can't just copy
the header file text wholesale.)
Disclaimer: I am not a lawyer; this is just my rough understanding of
things.
