Part of rev 19:10:

"Praise God, for the testimoney of Jesus is the spirit of prophecy."

"Mol Dia, Óir is í spiorad na fáidheadóireachda fianaise Íosa"

(Verb-predicate-subject)
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Chapter 8 of "Teach yourself Irish":
'If the subject and predicate are definite nouns, e.g. "Tom is the old Man", "John is my son", "The big book is the prize", then the order is: is é Tomás an sean-duine; is é Seán mo mhac; is é leabhar mór an duais"
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Shouldn't I put the definite article "an" before fianaise so that we have:

"Mol Dia, Óir is í spiorad na fáidheadóireachda an fianaise Íosa"

Also, why does "na" mean "of" here? Usually na is the plural of an. Couldn't I use "o" instead?

No, you shouldn't put an before fianaise. Just because a definite article is used or required in English, does not mean it is appropriate in Irish.

In Irish sentence structure it is incorrect to use two definite articles in a row where two nouns come together in a genitival construction like "spirit of prophesy". Generally, the article is used with the noun which is in the genitive case, and not the one which is in the (typically) nominative case. Hence, you get spiorad na fáidheadóireachda, lit. "spirit of the prophesy" rather than "the spirit of prophesy". In the case of fianaise Íosa, because Íosa is a proper noun, it doesn't take an article here even though it is in the genitive case, but if it were a regular noun the article would similarly precede it, not the nominative fianaise.

I think this partly answers your second question also, na does not mean "of" here, it is the definite article, "the". The English genitive marker "of" is built into the Irish noun fáidheadóireachda which is in the genitive case. What I would stress, though, is that while na is the plural of an when used with masculine nouns, this is not strictly true when used with feminine nouns. With feminine nouns an is the nominative singular form of the article, and na is both the genitive singular form, and the plural form. What you have here with na fáidheadóireachda is a singular definite article preceding a feminine noun in the genitive case, "of the prophesy". See The Grammar Wizard on teanglann.ie for more.

In Irish, you typically avoid joining two definite nouns together in the genitive (i.e. the one in the nominative tends to stay indefinite, and the genitive noun, or, in this case, the noun of possession becomes definite). Thus, you get fianaise Íosa (names are always definite).

As for your second question, the word na doesn't really mean 'of', like it does in English, it's just a form of the definite article that denotes the genitive case. Na is the feminine form of the genitive article, an being the masculine form. You can see the other forms of the article below:

Nominative Genitive Nominative pl. Genitive pl.

Masculine an an na na

Feminine an na na na


Notes:
an causes lenition when used as the masculine genitive singular form of the article
an causes lenition when used as the feminine nominative singular form of the article
na causes aspiration (h- prefix) when used as the feminine genitive singular form of the article
na causes aspiration (h- prefix) when used as the nominative plural form of the article (masculine and feminine)
na causes eclipses when used as the genitive plural form of the article (masculine and feminine)

fianaise Íosa means already THE testimony of Jesus. The name Íosa turns it into a definite noun phrase, so no definite article is necessary.

Of is a surrogate for genitive relations in English because the use of the English genitive ending "’s" is limited and a preposition "of" is used instead.
But Irish genitive is used without limitations and no surrogate prepositions are used, neither "ó" nor "de".

But nonetheless you are somewhat right in that the article in a definite noun phrase is a marker of genitive relations in Irish. "X an Y" (Y masculine singular genitive) or "X na Y" (Y feminine singular or masc./fem. plural genitive)
Both mean "the X of the Y" or "the Y’s X". (note: there is only one English article in the latter just as always in Irish)
So we get: spiorad na fáidheadóireachta = the spirit of the prophecy.

There is a tendency in English to put an article with the first noun only. But "the spirit of prophecy" does not mean "the spirit of a single prophecy" but of all prophecy, of prophecy in general. That is why it is definite in Irish: an fháidheadóireacht = "the prophecy".

The definite article with the first noun in Irish ("an XY") only occurs when the second (genitive) noun Y is clearly indefinite, merely like an adjective.

And again back to fianaise Íosa: In case Y is already a definite noun (like Íosa) no article at all is used: X Y = the X of Y (or: Y’s X, note: no article in English, too).

People should use the actual English genitive (ie. ’s genitive) much more often when explaining Irish – it works just almost identically to Irish genitive in terms of definiteness…

You say Jesus’s testimony and not *the Jesus’s testimony or *Jesus’s the testimony. Same in Irish, fianaise Íosa ‘Jesus’s testimony’, no article.

You say the fisher’s boat just as you say bád an iascaire, and you don’t say *the the fisher’s boat or *the fisher’s the boat – no double article, same in Irish.

There are languages which do this differently (Ancient Greek, for example, which says things along the lines of ‘the Hercule’s the club’ with genitive), but English and Irish both are really not dissimilar here.