> I hope you see it's getting complicated, and it's clear why non-native speaker would have issues here.
As a native English speaker, I recognized intrinsic complexity in the language early on during my learning journey. Perhaps this is why I do not judge non-native speakers harshly, preferring instead to appreciate their effort.
> Also, your explanation regarding Germany is wrong, because it falls apart when you apply it to "the Netherlands" or "the United States".
Both are plurals nouns, thus commonly requiring use of the definite article "the". Another example is the band "the Cars".
Again, an English proper noun which is comprised of four countries[0]. Just because a proper noun does not end with an 's' or 'es' does not mean it is singular. Some proper nouns end with an 's' or 'es' and are not plural. This is why one would not say "the Wales" even though it ends with 'es' as Wales is a proper noun identifying a single entity (country in this case).
Another example of this type of linguistic contradiction is "aircraft", whose plural is also "aircraft"[1]. So the following examples are grammatically correct:
An aircraft costs money to operate.
The aircraft did not pass inspection.
Multiple aircraft are more than one aircraft.
EDIT:
English is a context-dependent language, fraught with contradictions and special cases, let alone vagaries introduced with various dialects.
Remember that when you wrote:
... I can't tell when to use "a" and "the"
even if my life depended on it.
I sought to provide assistance in resolving this dilemma and nothing more. My hope is this thread has helped.
And before "the Netherlands" is brought up in comparison to "Wales", the etymology of the proper noun "Netherlands" should provide clarification:
The Netherlands formerly included Flanders and thus were
equivalent geographically and etymologically to the Low
Countries.[2]
Also, your explanation regarding Germany is wrong, because it falls apart when you apply it to "the Netherlands" or "the United States".