The question is a little complex, but perhaps not entirely for the reason you think.

In contemporary English we do not generally distinguish between a singular 2nd person and a plural 2nd person (you/you), except in some versions of English (you all, etc..). So historically speaking 'thou' is a 2nd person singular.

Hebrew, Greek, Latin all do have 2nd person singular/plural distinctions.

But singular/plural distinctions and informal/formal distinctions do not always overlap in the same way. If you'll indulge me for suggesting a wikipedia reference, you need to understand that the T-V distinction is both historically conditioned and historically diverse. Note carefully how it can express power dynamics as well as solidarity dynamics. As well as the fact that different parties can exert different force on the use of pronouns by the other party.

This carries into the question of Biblical Translation - the oldest translation tradition in English goes back to the KJV and the Tyndale version it largely relied upon (apart from the Wyclif translation which translated from the Latin); at a time when English still employed Thou as a separate pronoun. In the KJV you find 'Thou' both for God, and for 2nd person singular, without necessarily implying informality.

However, as both language developed and changed, as well as translations, in some English translations there was a choice to maintain 'thou' language for God, even when dropping it from other 2nd person singular usages (i.e. people). This used to be the case in the New American Standard Bible, which only in 1995 decided to eliminate Thou usage for God. The rationale for maintaining for so long was, if I recall correctly, that it expressed the intimacy of the relationship with God.

In answer to your final questions, yes there are Bible translations and languages that don't use informal pronouns for God. No, there's no 'official' ruling on the matter, who do you suppose would provide such an official ruling?

There is a certain amount of use of argot or jargon involved in maintaining the language of the King James version of the Bible - by using "thou," it marks you as a member of the "in-crowd" or someone who is a believer. So when people are parodying Biblical verse they will adopt this language to reflect it - see the Monty Python and the Holy Grail verses that lead to the throwing of the Holy Hand Grenade, which starts:

And Saint Attila raised the hand grenade up on high, saying, "O LORD, bless this Thy hand grenade that with it Thou mayest blow Thine enemies to tiny bits, in Thy mercy."

hi! there are some bible experts here, but it might be worth x-posting to /r/AcademicBiblical