Yes.
Makes a Copy of the Item
Minor Conjuration reads:
Starting at 2nd level when you select this school, you can use your action to conjure up an inanimate object in your hand or on the ground in an unoccupied space that you can see within 10 feet of you. This object can be no larger than 3 feet on a side and weigh no more than 10 pounds, and its form must be that of a nonmagical object that you have seen. The object is visibly magical, radiating dim light out to 5 feet.
- No Larger that 3 feet on each side - check.
- Weigh less than 10 pounds - check.
- nonmagical - See below.
- that you have seen - The one you have seen, not a type a facsimile of the one you seen - check.
Rules as Intended
Jeremy Crawford tweeted a ruling which at the time was an offical ruling (now unofficially) ruled that it is a magical facsimile:
Minor conjuration: object is 3 ft. on a side or less, period. Composition is DM's call. It's worth 0 gp; it's a magical facsimile.
Spell Books Are Non-Magical
The description of the Spellbook class feature reads:
At 1st level, you have a spellbook containing six 1st-level wizard spells of your choice. Your spellbook is the repository of the wizard spells you know, except your cantrips, which are fixed in your mind.
...
The spells that you add to your spellbook as you gain levels reflect the arcane research you conduct on your own, as well as intellectual breakthroughs you have had about the nature of the multiverse. You might find other spells during your adventures. You could discover a spell recorded on a scroll in an evil wizard’s chest, for example, or in a dusty tome in an ancient library.
...
The Book’s Appearance. Your spellbook is a unique compilation of spells, with its own decorative flourishes and margin notes. It might be a plain, functional leather volume that you received as a gift from your master, a finely bound gilt-edged tome you found in an ancient library, or even a loose collection of notes scrounged together after you lost your previous spellbook in a mishap.
The book description doesn't use the term magical in all of the descriptions of possible forms the book can take. Including the inks:
For each level of the spell, the process takes 2 hours and costs 50 gp. The cost represents material components you expend as you experiment with the spell to master it, as well as the fine inks you need to record it. Once you have spent this time and money, you can prepare the spell just like your other spells.
Rules as Intended
Jeremy Crawford also (now) unofficially ruled a spellbook isn't necessarily magical:
A normal spellbook or spellcasting focus is not a magic item. A magic one is possible, such as a magic staff.
So, together, we get an answer of yes. You can use Minor Conjuration to get a copy of a non-magical spellbook.
Would it be a Blank Book?
No. An object in D&D is defined:
For the purpose of these rules, an object is a discrete, inanimate item like a window, door, sword, book, table, chair, or stone, not a building or a vehicle that is composed of many other objects.
Words are not discrete items, so are not objects in themselves. They become a part of the book when they are written in them. Aruging otherwise would be arguing that if you targeted a book (an object) with spells that target one object like disintegrate or true polymorph, would somehow leave the words separate from the book.
An update to that, is that the latest version of Sage Advice carries this question:
Can Minor Conjuration create a copy of a book, complete with all its text, if the wizard hasn’t seen all the text?
No. In the case of a multipart object, the intent is that you must
have seen all parts of the object to duplicate those parts. In the
case of a book, if you have seen only the cover, then the duplicate
created will be a copy of the cover, and the pages will be blank."
The practical upshot, is the Wizard should still be able to replicate his SpellBook, having seen all of it. But walking into a library once wouldn't allow him to conjure any and all titles of all the books. This seems like a reasonable compromise position, but still leaves he answer to the question: yes.
Yes (no other requirements)
The text for this feature clearly spells out the limitations for items it can conjure:
This object can be no larger than 3 feet on a side and weigh no more than 10 pounds, and its form must be that of a non magical object that you have seen.
A key will easily fit the size requirements, so as long as it is not magical and the Wizard has seen it, then Minor Conjuration should have no problem creating a replica.
Best Answer
"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, rules guru for 5e, clarified in an unofficial tweet that using a minor conjuration weapon won't damage and dispel it:
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 dispel 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.