The Haikyuu anime tries to be as faithful as possible to the manga. It might compress or reorder some elements for the sake of pacing, but outright skipping of parts is rare. Fans usually feel that the anime does justice to the original manga.
In general, the Haikyuu anime doesn't skip significant sections of the manga. It does make some minor adjustments for better animation and storytelling, but the core plot and important events are all covered.
No, it doesn't. The anime adaptation is quite comprehensive and doesn't skip major parts of the manga.