Are Texas schools required to display posters with an Arabic translation of "In God We Trust"?
No. The activist (Chaz Stevens?) not only misses the legislative intent behind the motto, but it actually would be a violation of the Establishment Clause if a government displayed the flags he donated.
Is there any case law that corroborates the implicit claim that sentences in these kind of laws should be interpreted as referring to those sentences or a translation of those sentences into another language, instead of to simply those sentences as rendered in the law, in English?
In the particular case of "In God We Trust", the legislative intent is very specific about the language in which the motto is to be displayed. See Aronow v. U.S., 432 F.2d 242 n.3 (1970):
It will be of great spiritual and psychological value to our country
to have a clearly designated national motto of inspirational quality
in plain, popularly accepted English.
(emphasis added, citing House Report No. 1959. 1956 Cong. & Admin.News, p. 3720).
The legend in the activist's flags is in Arabic, and therefore not in plain, popularly accepted English.
The activist's purpose would violate the Establishment Clause because the legend in the activist's flag is less religion-neutral than the national motto. The transliteration of the legend at issue is nakhnu nathaq bi-(Al)lahi (I might be wrong in some vocals of the middle word), thereby making an unequivocal reference to Allah, the god of muslims. This might amount to governmental sponsorship of a religion, the Islam, insofar as in the English language, the word generally refers to God in Islam. Neutrality would require the legend to be nakhnu nathaq bi-(a)l-ilahi ( نحن نثق بالاه), since ilah means [a] god.
Although "God" in uppercase and used as proper noun is attached to judeo-christian theology, this religious bias is historically perceived as rather negligible when compared with the practicality of inspiring "patriotism" and akin values. See, for instance, Aronow at 243 and n.2. Similarly, Gaylord v. U.S., 74 F.3d 214, 216-217 (1996):
a reasonable observer, aware of the purpose, context, and history of
the phrase "In God we trust," would not consider its use or its
reproduction on U.S. currency to be an endorsement of religion.
Linguistically, the activist's legend even alters the emphasis of the national motto. By starting with nakhnu (which means "we"), the import of the legend is that "We, not others, are the ones who trust Allah". By contrast, the national of the motto connotes an emphasis on the noun "God", not on "we". To preserve the emphasis the national motto makes, the activist's legend should have been bi-(a)l-ilahi nathaq or something close thereto.
