"Damage" isn't damage
If you have to put "damage" in scare quotes, it's not damage. Dipping a quill in ink doesn't damage ink, it just moves it about.
Conjuring a weapon
Using a minor conjuration dagger in combat is less certain, because "normal wear and tear" for a blade is nicks and chips, which is non-catastrophic damage, but is indeed damage instead of "damage" and will destroy a blade over time. Except that D&D doesn't normally care about wear and tear at all, even for weapons, and only cares about actual hit points of damage that structurally undermine objects.
D&D Designer Jeremy Crawford, official rules guru for 5e, clarified that using a minor conjuration weapon won't damage and dispell it:
Dario Berto @Uzedh · May 5
@JeremyECrawford If I conjure a weapon with Minor Conjuration and I hit a creature, does the weapon take a sort of damage to disappear?
2:59 PM - 9 May 2016
So that's the official word.
But personally, I still think this falls into the realm of DM's judgement. Fifth Edition is designed around the principle that words mean what they mean ("natural language"), and that DMs are the local arbiters of the game's words so that they make sense for the game they're running. DMs are given, by the game's RAW, the responsibility and empowerment to figure out how to apply the meaning of words the game uses within the imaginary world.
This principle means it's possible that in one DM's world, deliberately or accidentally scratching a minor conjuration does dispell it. That DM's world is one in which conjurations are mystically fragile objects. In such a DM's world, Minor Conjuration wouldn't be useful for weapons, except perhaps if you were bluffing with them to appear armed when you're not. Another DM's world (Crawford's definitely!) might equally allow for cosmetic damage to be merely "damage" that doesn't count as actual damage. I expect most DMs are going to fall on the same side as Crawford and allow minor conjuration weapons to be useful.
The meaning of "object"
As for whether "an object" means a single object: yes, that's what the words normally mean. Since the ability's description doesn't include words that mean otherwise, Minor Conjuration is limited to creation "an object". Being listed for purchasing purposes in the equipment section doesn't have any significance beyond that you buy them as a bundle, so has no relevance for deciding the difference between an object and multiple objects.
Radiating dim light
Again, this does what it says on the tin. Dim light is dim. A smartphone screen radiates dim light, enough that you can use it as a (poor) flashlight at night. But does the light a smartphone shed light up a surface that's already lit up by sunshine? No, but it might be visible within a slight shadow, or under the chin of someone using the phone. Dim light is just that: dim, and only dimly visible, unless you're looking carefully and the conditions are suitable to noticing the dim illumination.
For an example of how it might be notable, but only barely, a conjured dagger in-hand might look "off": real-world light interacts in complicated way with objects, and adding even a dim light source changes the appearance of nearby objects in ways that, today, divide "good" computer graphics from "fake looking" ones. A dagger in hand, glowing even slightly, will change the appearance of the shadows in the folds of the fist curled around its hilt, providing a clue that astute observers can pick up on. Again, this sort of thing is up to the DM to read and apply to the game world according to their judgement; so it does what it says on the tin, and the application of the words on the tin to specific or unusual situations are the DM's responsibility and privilege.