There is no magical damage type in D&D 5e
A dagger does piercing damage whether it is a magic dagger or no. A dagger made by Minor Conjuration is magical - it says it is in the text.
If a creature has immunity/resistance to piercing damage than every dagger is going to be subject to it.
If a creature has immunity/resistance to piercing damage from not X, then if the dagger is X it will not be subject to it.
For example, a werewolf has "Damage Immunities bludgeoning, piercing, and slashing from nonmagical attacks not made with silvered weapons." So if the dagger is magical (which it is) or silver (which it could be if you made it so) it will overcome this resistance.
If the creature is unwilling then nothing happens
Dnd 5e operates on the principle that things only do what they say they do. Jeremy Crawford, lead rules designer for 5e, and known for adjudicating rulings on Twitter, has stated:
Beware of claims that a rule does something mentioned nowhere in that rule or elsewhere in the core books. There aren't secret rules. (source)
See this question, for further reference.
Following this principle, if the designers had meant a School of Conjuration Wizard to be able to swap places with an unwilling creature, subject to a saving throw, they would have stated so in the ability description. So, RAW swapping places with an unwilling creature, using this ability is impossible.
Further support for this conclusion has been suggested by mxyzplk, in the comments:
...this is why the word 'Benign' is in the name. In 3.5 there is in addition a 'Baleful' Transposition that does operate on an unwilling subject.
And, if you try, you'll probably lose your action.
If a PC wanted to try and do this, then it would be up to the benevolence of their DM as to whether they either simply "realise on reflection that such a course of action is impossible", or they lose their action that turn by trying to do it unsuccessfully.
Xanathar's Guide to Everything is an optional rules source, but it provides details on what would happen when a player tries to Cast a Spell on an invalid target.
Invalid Spell Targets (XGtE p. 86)
... If you cast a spell on someone or something that can't
be affected by the spell, nothing happens to that target,
but if you used a spell slot to cast the spell, the slot is
still expended. ...
Benign Transposition is a class ability rather than a Spell, but it seems logical that a failed use of it would follow a similar pattern - your action and one usage of the ability would be consumed, despite the failiure.
Could you 'homebrew' transposing an unwilling creature as possible?
In your own game your DM is welcome to rule entirely as they like, and in that case maybe a Charisma save might be argued to be appropriate for the unwilling creature (similar to the spell Banish)? However I would personally advise against this ruling. I think it would add a great deal of power to this ability and probably unbalance it.
Best Answer
Minor conjuration can be done about every 6 seconds
By default, PCs can perform 1 action per round and each round is approximately 6 seconds long. Thus, it would be possible for the 2nd level wizard to perform a minor conjuration about every 6 seconds by consuming their action. If the wizard obtains a way to gain additional actions per turn that they can use to perform minor conjuration, then the amount of times it can be done is multiplied accordingly.
There is no other limitation to how often they can perform it.
Minor conjuration is not a spell and does not interact at all with a spellbook
Minor conjuration is not a cantrip or any other type of spell; it is a class feature. Thus it does not get written into a spellbook nor does it cost spell slots. Losing your spellbook will not impair your ability to do this either. In fact, as written, only one thing is required to perform minor conjuration: an available action. Nothing else matters.