I think the title says everything.

If I've a ward in a area with background count (acpected). Is the BG subtracted (added) from the ward's force?
And in combination with this. If I use ritual magic to target someone in a BG area and within a ward. Are both added up, or is the BG not important because it's not at the location where the spell is casted?

If the BC is aspected to the tradition of the person who set up the ward, nothing really happens. The caster gets a dicepool bonus added when he applies the ward, but nothing further happens.

If the BC is not of the mage's tradtition, he gets a penalty to his magic, as described, and the ward he can set up is significantly lower in force.

If the BC is added after a ward is up and the BC is not aspected to the tradition, it reduces the force of the ward, potentially disrupting it.

(all this is from page 118, Street Magic)

If someone is casting into an area of BC that is not aspected for them, and the target is behind a ward, then the force of their spell is affected by the BC, and then the target gets a dicepool bonus on his Resistance Test equal to the Ward's Force.