[Pathos]

During the character creation one of the players created a mage whose temple was attacked by a dragon. During the attack the mage loss his right leg and arm. Accordign to his backstory,  the mage salvaged parts from his destroyed temple and made a replacement arm and leg, fused together by "magic".  Being the noob Game Master I am, I okayed his creation without taking the necessary essence deduction.

The mage argues that becuase his replacement parts don't give him a benefit like standard augmentation, that he shouldn't be penalized on his essence.  According to him, the stone/metal replacement bodyparts have no mass or density and do not contribute to his composite body weight. It is all fused together from magic from an unamed inifite source.  It does not negatively affect any attributes of body or agility. It just makes him "normal". 
My questions:

1. Should I have taken an Essence Deduction as he is not a "whole" person? 
2. Should I take into account his stone/metal appendages when completing stealth, body,  and agility test?

[Lethe]

You don't get essence reduction for just losing a limb, but would for implanting an artificial one.

If he just wants to be special, but no ingame advantages out of it, which you have to make very clear to him, then it should be fine. The limbs could get hold together by an unique focus inside the limbs, that can't be used for anything else.

But it shouldn't make him immune to anything, the less of weight will not effect any of his abilities, the limbs can still break, get wounded etc.

Don't let him later fight arguments with "but the magic of my limbs..."

[beowulf_of_wa]

even if you don't give any "normal" disadvantages, being a creature that obviously discovered a new form of metamagic usable by non-initiates makes him the top of many target lists, most of whom would love to study him in various tests, few of which would be anywhere near pleasant. (think of it as the same experiments that corps were/are doing to technomancers)

[KommissarK]

GMs should never punish players for style.

That said, if you're OK with this rather special snowflake, I don't see a mechanical reason to punish him. If you do punish him for it, it would necessarily need to have some sort of benefit for him (if he had it before start of play).

[UmaroVI]

You can also get cloned body part replacements for no loss of essence. It's not losing the arm that causes the essence hit; it's that when you install the cyberarm, Dunkelzahn demands your point of holistic well-being.

[The Wyrm Ouroboros]

According to him, the stone/metal replacement bodyparts have no mass or density and do not contribute to his composite body weight.

I'm all for interesting.  I'm not for 'crap you couldn't do sober, healthy, and with twenty years to make it work'.  I'm good with letting him have spirit/magic-infused replacements for his limbs; insert my evil GM smile, because doing that is going to get magic-research people Very Interested Indeed.  But you should inform him if they have no mass or density, contributing nothing to his weight, he's going to have to make an Agility (2) test to take a step.  And again to take another one.  And again ... you get the idea.  He may mean no additional mass/density beyond what his ordinary fleshy limbs were, but I'd still give him the option to either have them at the 30kg weight of a stone leg and the 15kg weight of a stone arm, or else be running with a constant dice pool penalty for sustaining a spell -- levitate, or something similar.

Cool stuff is cool.  It also has built-in disadvantages.

My questions:
1. Should I have taken an Essence Deduction as he is not a "whole" person? 
2. Should I take into account his stone/metal appendages when completing stealth, body,  and agility test?

See others' commentaries above.  My replies are 1) yes, and 2) yes.  If not, well ...

GM tip: give the players one (1) chance to convince you.  Inform them of this fact at campaign start, and that if they don't make an absolutely compelling argument, then your adjudication stands.  You may, if you are feeling kind, inform him of the consequences of his desires.  "Magic limbs with no weight and no essence loss!!" equals 'GM is sending snatch teams after my character twice every session, and once in-between runs."  By Run #5, they'll be kill teams with orders to just bring back the limbs.  If by some miracle he remains alive and free by Run #10, pull out all the stops -- kill / blackmail all of his contacts, all of his friends, blow up his favorite bar, send a mage-defended attack helo after him on the I-5 bridge to blow his ass into puree.  Have corporate mage-research VPs make calls to his teammates, offering direct bounties on his head -- or at least his limbs.  If they don't play ball, then kill his teammate's contacts.

Cool stuff is cool.  A player should always be aware, though, that other people want the Cool, and every GM should make that a major point.  When a GM says 'Okay!' to a player saying 'I'm neat!', the player should get nervous.