Uhhh no. First, it's an activated ability. Second, it's used from the graveyard and not the library.

Is unearth a spell?

As mentioned, this is an activated ability and not a spell. This means that a player cannot use effects that counter spells to prevent the unearth ability from resolving.

Is unearth a sorcery?

Unearth only as a sorcery.) Unearth is a keyword ability introduced in Shards of Alara as the Grixis signature mechanic.