Mana Tempest interactions

I was wondering about 2 interactions which are hard to test...

1) with Archmage
I know that Archmage does increase the mana cost of mana tempest passiveley since the spells have higher mana cost and therefore mana tempest has a higher cost too.
I was wondering if archmage increases the mana cost of tempest a 2nd time by increasing the mana costs of a) the tempest and b) the spells cast inside

2) with Arc
Arc gets bonus dmg for chains and chains 3 times. My tempest now gives +3 chains but the skills will not chain further.
As far as I understand it it could be
a) Arc now has 6 chains but only chains 3 times since it "stops" after 3 but still has chains left over
b) the chains get "reduced / fixed" to 3 chains from tempest and there is no bonus
Would be important to know for bosses