First i want to say that my english is not that great, you been warned. The Novel explain everything with much detail, so i recomend reading it.
The Falna actually affects the overoverall power.
The Falna is a blessing tha increased the power of mortals, it their god dies the falna is then sealed, they don't lose their levels, skills and others, but they become unable to use them. Killing their god will make them weaker than a level 1. They have to convert to other god to access their Falna again. But in this case is more probable that they will be we wipe out be Ares family, before they obtain another God.
The case with Welf and Mikoto was that their gods simple open their Falna, thus making Hestia able to overwrite their old falna with a a new one.
In a open state the mortal Falna is independent of their gods, like in Ryuu case, they can keep their power, but they can't increased it without a god help. They need a god to become stronger.