[Hermann the Cherusker]

In this particular case as well, owing to the fact that the first husband was Japanese and likely not Catholic (since we are making so many other suppositions), a decree of nullity could be granted on those grounds alone, regardless of adultery or anything else.

No, it could not. You simply don't understand canon law.

[Burkean]

Presuming the first husband was not Catholic, and further presuming that the marriage was not celebrated before a priest, there would be no need for a Declaration of Nullity because they would not be considered duly married in the eyes of the church.

I don't know if it's up to each diocese or what, or whether you are reading very old Canon law (the Council of Trent that you cite is 16th century, and there have been a multitude of changes since then, like it or not).

There is most certainly a procedure for what is commonly called an anullment, officially called a Declaration of Nullity. The grounds basically are described as that there was no "real" marriage in the first place, and it has been variously defined according to each case.

It's not always granted, but it is most certainly granted at present more often than it was granted in the 16th century.