Do Physical Armor (Mage Spell) and Mystic Armor (Adept Power) stack with each other?

I believe so.

Absolutely. See the FAQ.

Yes. And both stack with worn armor.

Including everything else that isn't worn armor. Get those cyberlimbs armored up if you want to tank it out.

Aye... i always see it as having different "Armor - Slots" and (it never came up), would only allow stacking so far (For example an possessed Ki-adept might push it).

1. Skeleton (Lacing, Density)
2. Intrinsic (Ki-Power, Spirit Armor)
3. Replacement Structure (Cyberlimbs)
4. Skin (Dermal plating, Orthoskin, Nanoskin)
5. Second Skin (FFBA, Whatever plugsuit-Fetishists wear)
6. Worn Armour in different layers
7. Extra Plates and Cushions (PPP-System, Kid with a Cushion on his tummy)
8. Personal Force-Fields (Armor Spell, Futuristic non-existing Forcefields)
9. Cover and Physical Barriers spells

And pretty much all stack. There are characters out there having more armour naked as a normal dude in a military powerarmour.

btw hate all the guys referring to runners having more armor than bloody tanks. sure you can get cyberlimbs with lots of armor and then let the mage cast armor on you and be possessed b a spirit. but so can the tank. A F6 spirit possessing a tank while using Concealment, Silence and Guard on it while the summoner sustains an Armor spell and a Reinforce spell on the tank and stunballs all astral attackers. That's not much of an investment for the military, if the GM thinks the runners are exaggerating...

A tank would just get half benefit from ItNW. 12 hardened armor would just add 12 dice to the 20 hardened armor it already has. The main benefit of acquiring hardened armor is lost on it.
Also, mages are rare. Combat mages more so. Yes, even in the military. Keeping a mage on staff just to buff up a tank would be a waste of important resources, cost-benefit wise. Very rare cases excepted.

Wouldn´t it?

Well yes. In the actual armour department. The ItnW would do little indeed though. The tank's already armoured. And the main reson why people want the possession armour is the hardened quality of it. To my experience anyway.
Since the easiest way of getting actual armour up is a matter of plating limbs. But that leaves you tremendously vulnerable to stun damage.

But you usually add the hardened armor to your regular armor if the power of the attack exceeds you Hardened rating. If you already are armored the hardened way, shouldn´t it stack? It would at least give the benefit of additional standard armor (which means more dice). So it is not bad, no matter how you see it.

True enough ^^

Edit: Never Mind...

If a player starts getting 20+ armor in my games, I start using mana bolts, gas, and acid attacks.

Right. There is always a way to bypass protection and you cannot be strong in every field.

Or just use Bind spells, Confusion, etc. It doesn't matter if you're functionally invulnerable if you can't do anything but sit there and wait for the sec teams to bring some diamond-bit mining drills over.

Using the Toxic Wave spells aspected to guns and/or armor is a great way to teach players a message, and if they complain, ask them if they really though Knight Errant public security mages didn't have those spells.

while this is a nice idea fluffwise, raw-wise runners will just dodge the first wave and shoot the mage in their first possible pass. in case they don't dodge, the mage still needs at least one more hit as guns are not made of sugar

Dodging spells is rather difficult, especially if the mage isn't protecting the team with counterspelling at the moment, and a good mage could kill guns with a single acid spell, and even if they didn't acid's secondary effects tend to cause significant damage to objects even it they don't destroy them.

Can't be done. Acid Wave is a chemical attack produced by magic, not a magical attack that acts like a chemical. It produces a liquid with extremely low PH and hurls it at the target. It is this liquid that does the damage, not the spell itself. You can't create an acid that's aspected to guns using magic any more than you could do so in a lab. If you're throwing out chemicals that are as reactive as those made by the acid spell, then you're going to melt your target's face along with his gun.

If you want something to just destroy weapons and armor go with a limited target Powerball.

Actually, it can be done, that is why it is called Magic... Regardless of whether it makes any sense or not (which I agree with you, it does not).

For my taste, though, I would just use "Wreck: Guns"... Simple and expedient. And you likely need only 3 Hits to damage the weapon (Weapon's OR) .

Personally, though, while I would allow a limited-target powerball to affect, say, plastics, or metal, I wouldn't allow it to affect "weapons and armor". That's like letting a spell affect "ghouls and drakes".

Personally, though, I think Knight Errant, at least, would be likelier to use an illusion spells such as hot potato - destroying someone's guns and armor is destroying evidence. And gangs wouldn't use it - it would be destroying spoils of war. So the only ones that might use it regularly would be corporate security, and even then if you are casting spells, you more or less have a bajillion ways to bypass armor already.

Points Taken... All very true indeed...
Most runners don't really give a damn about the oppositions armor or weapons, though (at least at our table anyways), so Wreck: Armor, or Wreck: Guns works very well for them in that case. Cannot remember off the top of my head if Wreck is the AOE version of the Spell or not... *shrug* The AOE version takes care of all visible versions of the Chosen Target, all at once, so only a single casting, rather than a handful...

there's always the Slay [Dragon] Spell...(SM p165)
and ofc there's the acidic weapons attacking spell: Corrode/Melt/Sludge [Object] (SM p166)

but a gun has a structure and armor rating like everything in the world. As it's an indirect Combat Spell, the holder of the gun may dodge, but won't get hurt, if he doesn't manage. The gun (=barrier) rolls armor (probably Reinforced Material: 8 ) AP is ignored (SR4A p167). If Force+net hits > Structure (9) gun is destroyed.

Do guns with structure damage impose a dice pool penalty on the wielder when fired?

Just like a car with structure damage would impose a penalty for piloting...