This seems neither very clear, nor internally consistent. Let's try and see which tests may or may not be affected:
Sadly the editing is bad and so it's not very consistent, but it seems that generally the Magic Rating is capitalized while magic as a concept is not. This grammar based interpretation would mean that everything that is related to the concept of magic (and that includes every roll of dice) is affected. Personally, I doubt that is the intent.
A background count impose a negative dice pool penalty equal to its rating for all tests linked in any way to magic (such as spellcasting, summoning, and skill tests that use active adept powers such as Killing Hands or Improved Sense).
p. 32 SG
1. Every test that includes the
Magic Attribute is affected. No exceptions. In your list, that would be: Spellcasting, Summoning, Binding, Dispelling, Banishing, Disenchanting.
2. Skill tests that are affected by adept powers. Killing hands is a weird example here because it doesn't actually affect a skill test, it determines what happens in the aftermath of one.
3. Drain is a double attribute test that is generally not modified by anything.
4. Counterspelling has Magic as it's linked attribute but the Counterspelling dice pool is not a skill test. It should not be affected.
5. Magic resistance tests are double attribute tests and decidedly mundane. Not affected.
Dual-natured creatures or purely astral creatures take a negative dice pool penalty to all actions equal to the background count.
p. 32 SG
Spirits get their force reduced unless acclimated. Resist Dispelling / Banishing is not affected directly, but both are based on force and force is reduced.
Pre-existing active foci, sustained spells, quickened/anchored spells and rituals are reduced by the background count. If they are reduced to 0 or less, spells fizzle, wards and rituals collapse, foci deactivate. A foci cannot activate while under the influence of the background count.
p. 32 SG
This is where limits become incredibly important. Spells get their force reduced by the background count and reducing the force reduces the limit. Reducing the limit reduces the hits that are allowed for the spell. This leads to quite a few interesting effects:
1. Spells that go below their threshold do not fizzle but cease to function.
2. Increase Attribute spells require their force to be above the attribute. If BC reduces the force to equal or lower than the attribute, the spell ceases to function.
3. Spells area of effect is reduced if the effect depended on hits or force.
Adept initiative is the trickiest of things. Personally, I don't think it is supposed to be affected because adept powers are basically an adepts cyberware. Turning of a samurai's wireless smartlink bonus due to matrix noise is one thing, deactivating his reflex booster anther. In that vein, disabling the skill bonus is equal to the smartlink but disabling the reflexes is kind of neutering the character.
Personally I think, BC is a badly designed concept. If should be a simple -1/-2/-3/-6 like ranges and equal bonuses for acclimated beings in their respective zone. Fighting a toxic spirit in Chernobyl should be hard because you're in the heart of it's domain and its strong there. Not because you're weakened and beaten by a spirit that could never hurt you otherwise.
I do like the fact that a background count of one is basically a munchkin killer though. Fun little example:
Examples include an isolated violent crime or love affair, [...]
So, lets assume a mage uses a F1 sustaining focus to keep a physical mask spells going. He uses that to get a mark on a date. At some point of the date either of them feels the butterfly in their stomach... and the focus deactivates. Or he kills him/her and the focus deactivates revealing his identity.