I am unsure about your data structures, because choice of structure makes a huge difference when doing this kind of thing.
Also, you need to learn more. Google around “affine transformations”.
> first point as first vector base, second point as first vector end AND second
> vector base, etc
I do not follow, provide an example
> I need to know the minimal and maximal coordinate points
¿the bounding box? ¿axis aligned?
> I only know that rotation matrix using quaternion should be applied in the process
I fail to see why
also, ¿rotation matrix or quaternion?
> Also I should not that vector normalization operation will be done too before this.
¡great! ¿what for?