How interchangeable are の／である／なる／たる when qualifying nouns?

Question

So we know that we can qualify/equate two things with a の.

• 友達のジョン　→　My friend John
• 先生の山田さん　→　A/My teacher Ms. Yamada
• 勝利者の亀さん　→　The winner: the turtle (as opposed to the hare)

It seems like most of the time, the の can be replaced with である without any change in meaning. Or is there some nuance where the meaning changes slightly? With 先生の山田さん, to me it has more of the sense of my teacher, whereas 先生である山田さん definitely does not. Does the である necessarily diminish the personal-ness of the qualification, or does it just depend on what you happen to be talking about?

Further, we can go on to include the なる connector as I discuss somewhat in this topic (“Grammatically-correct” particle-less phrases/sayings). なる appears to add a little more formality, but other than that I can't really see what else it brings to the table. For example, in my Japanese Bible, I've seen the following when referring to God:

• 父なる神様　→　God the/our Father; Father God
• 神なる主【しゅ】　→　Our Lord God

If I recall correctly, these were both instances (although appearing multiple times in the whole Bible) where someone was referring to God while speaking to other people. Is this likely just due to a different writing style by different Biblical authors, or is there really some subtle difference in meaning?

Finally, there is たる which seems to be the most formal (?), most archaic (?), and mostly literary (?). Again, all I can tell is that I usually see this paired with some kind of recommendation / moral suggestion / responsibility.

• 教師たる者、忍耐力がなくてはならない　→　All teachers must have patience
• 学生たるもの、勉強すべきである　→　All students should study

Obviously if the meaning changes completely they are not interchangeable.

• (社長たる道　=　社長の道)　≠　社長である道　≠　社長なる道
  • Doesn't work because we're showing a possessive with the の, not equating.

So at what times are these connectors interchangeable, and what nuance(s) does each bring? Is my reasoning correct in any of these areas?

Answer 1

These are my thoughts.

友達のジョン　→　My friend John
先生の山田さん　→　A/My teacher Ms. Yamada
勝利者の亀さん　→　The winner: the turtle (as opposed to the hare)

These are all adnominal copulas historically coming from the defective Old Japanese copula, に (infinitive), にて (continuative), にあり (conclusive), の (adnominal).

It can be replaced with である, but である has a slightly more literary/formal feeling. That is the only difference in my (non-native) opinion.

父なる神様　→　God the/our Father; Father God

This is the adnominal form of one of the Classical Japanese copula, なり (coming from に + あり). It has a more historical/old feel to it than である.

教師たる者、忍耐力がなくてはならない →　All teachers must have patience

This is the adnominal form of the other Classical Japanese copula, たり (coming from と + あり). My feeling is that it has an even more archaic feel to it than なり. Historically, the difference between it and なり was that it expressed something temporary and なり expressed something permanent, but I do not think that distinction exists in Modern Japanese.