I've been wondering if vassals are counted as allies in Humankind and give bonuses to your empire? Like for example I choose to be the Umayyads which has the legacy trait learned friends that gives you +5 Science per alliance on all cities and I have no allies but two vassals, will my two vassals count as allies and give me +10 Science for all my cities?  

Nope, Vassal is a separate category. Check the British culture for a bonus that is related only to Vassals.

Thanks for the info, that really fixes it for me. Such a great game by the way really enjoying it.

Sure of that? The achievement related to having lots of allies triggered when I vassalized all other factions.