2. Would you allow the above Warrior mage in full armor to benefit from both the DB of the mundane armor and the Steel Skin spell?
Yes. Steel Skin is magical armor and stacks with non-magical armor. It doesn't stack with itself or the other variations of the same spell with different names (Stone Skin, Tree Skin, Mage Armor, etc), same as physical armor doesn't stack with other actual armor.
Similarly, it stacks with taking cover behind a wall or something.
It also stacks with different spells that increase DB in different ways (e.g. Magic Shield, Mantlet, Blur, Bladeturn, Deflections, Boost Qu, and Boost Ag with the Swashbuckler talent, etc).
Wearing mundane armor causes all spells (incl. Steel Skin) to cost more PP and incurs a casting penalty. A minimum of +2 PP per spell and -10 to casting rolls (for a suit of Soft Leather) unless you carefully optimise Armor By The Piece (and that will leave certain locations unprotected if you're using hit locations)
Also, the extra +2 PP will often make a spell take an extra round to cast - casting time is 1 round per 5 PP.
3. If, on the other hand, you grant the Warrior Mage both bonuses from the mundane and the magical armor, how do you balance Steel Skin against Magic Shield?
The same way you "balance" wearing real armor and carrying a real shield. i.e. there's no need to do anything, it already has a built-in cost.
A real shield is more weight/encumbrance and ties up an arm/hand (i.e. no two-handed weapons with a shield. It's hard to climb or do lots of other things one-handed too). Magic Shield costs PP and time to cast. Casting both Steel Skin and Magic Shield on yourself wastes the first round or two (or more) of Steel Skin while you're casting Magic Shield....an unlucky Crit could kill you in that time.
Why, having both spell available, a mage warrior would learn and invest (or teach even) a spell like Magic Shield?
For the same reason a Fighter might choose to wear full Plate
and carry a shield, and wield a 1H Sword or Mace, with maybe a backup Main Gauche in case their shield gets broken.
Some other fighter might opt for the same armor with a 2H Sword or Battle Axe and the Blade Barrier skill instead of a shield.
And another might choose a Bastard sword, and switch between 2H and 1H styles, with optional parrying dagger and maybe a Battle Rune of Magic Shield or Bladeturn.
Every option has a cost (even if it's only the opportunity cost of not doing something else) and players will make their own choices as to whether that cost is worth paying in the current circumstances.