Spell Damage Increase

Do extra damage die gained from abilities(Beast Lore, Leader)&advantage apply to spells as well?

Beast Lore is written "The character now deals +1D4 additional damage to monster..." - Core Book, page 115. Leader and Advantage on the other hand is as the character's attacks deal additional xDx dmg. So I quess my question really is: Are spells considered as attacks?

On the same subject if spell caster attacks from advantage does he/she get +2 to resolute test?