1. On wowhead/thottbot there are effects listed for spells, for example "Apply Aura: Mod Speed Slow Value: -40" for frostbolt.

    Does anyone know if it is possible to get this information through the API, or if not, how they do it?

    This information is not available via the API. I do not specifically how they obtain this information, but it almost certainly involves parsing the data cache.