Dōnum is neuter; amīcus, fīlius, and ager are masculine. Neuter nouns are always the same in both the nominative and accusative case, in both singular and plural. See this question for more about how universal this is.
Here are some more neuter nouns that you may be familiar with (from early chapters in Lingua Latina Per Se Illustrata):
Baculum dominī in ...
It's not that esse takes the accusative—it's that cupiō takes the accusative, and esse links two things in the same case. In other words, regem is accusative because mē is accusative, and mē is accusative as the object of cupiunt.
This is a fairly common construction in Latin, called the "accusative with infinitive" (or accusativus cum infinitivō ...
This is called a nominativus cum infinitivo, which is possible with intellegitur because the finite verb is passive. Debeo normally has a mere infinitive with it, so there is no indirect statement there either. There is no indirect speech, no accusativus cum infinitivo.
An a.c.i. cuts through the sentence, separating main clause from indirect statement, such ...
As a general first note, praestandi looks much more like a gerund than a gerundive here.
A gerundive would be passive in nature.
A gerund is active; it is best understood as a case inflection of the infinitive.
If praestare is "to excel", then praestandi is roughly "of excelling".
For example, ars magna scribendi is "the art of ...
Cupere is a special kind of verb. You can use it to talk about something the subject of the sentence wishes to do himself. In that case you use an infinitive as the object and predicate nouns or adjectives are in the nominative:
Cupit rex esse.
He wants to be king.
Normal objects are in the accusative as usual, though:
Cupio placentam edere.
I want to eat ...
In bonis means "among (the) good things": that is, the gift of breath is considered to be among / in the category of things that are good.
Bonum could have been used and would be grammatically correct, but gives a slightly different meaning, simply "considered good / a good thing" without any added sense that there is a definable class of ...
I made a corpus search for per near -ndum in Cicero and found no hits for per with an accusative gerund.
Without the restriction to Cicero there are too many hits for me to wade through now.
I don't recall ever seeing per with a gerund, so I would recommend against it.
There is an idiomatic and common way to say "through doing":
It is not *per ...
Feels a little cheap as an answer here, but the auto-generated Related Links suggests to me the excellent Was “Pascha” ever used as a neuter first-declension noun? which provides a possible example of an exception here. Absolutely none of this answer is original research, I am merely reporting what I see in that question and its answers.
Notably, the ...
According to John Jackson, later editions have an alternate reading:
Hunc ergo ordinem Romanis quoque imitari placuit, sed frustra, quippe
fugit eos unum diem, sicut admonuimus, additum esse ad Graecum numerum
in honorem imparis numeri.
Jackson notes: "the common and later Editions read esse instead of a se, which latter is evidently the true Reading; ...
Indeed something fled the Romans, and that something was expressed by accusativus cum infinitivo.
The key is to supply the implicit esse explicitly with the past participle:
fugit eos deum unum additum [esse]
it escaped them that a god had been added
Now deum (or diem if we are to read it as "day") is the subject of esse and things start falling ...