Laisser pleuvoir du feu.

I think it fits most with 2 and 3. Here, “laisser pleuvoir du feu” means there will be a rain made of fire, in an apocalyptic meaning.
du feu is a COD (Complément d’Objet Direct), beacause you can ask

Laisser pleuvoir quoi ? Du feu

You will find the same structure in those sentences:

pour laisser passer le train
pour laisser couler de l’eau

You use “du” because “water” and “fire” are not countable.
Whereas you use “le” because a train is countable.
So “du” has the meaning of “some” here (maybe you could say “let rain some fire” ?)

Then God let it rain

You would say one of those:

Alors Dieu laissa pleuvoir (a bit odd)
Alors Dieu laissa la pluie tomber

You only use “le Dieu” if you want to stress the fact there is only 1 God. Otherwise, “Dieu” is a proper name.

The good meaning is your number 1.

Du is a partitive article.

One can also say: la neige, or de la neige, du feu, or le feu, …

Du feu is subject of pleuvoir.

Laisser is a semi-auxiliaire (like faire, voir, regarder, entendre, sentir )

Le bon usage 14, 821 f.

See also: http://www.etudes-litteraires.com/forum/topic11075-faire-infinitif-expose.html

I propose two meanings for ‘Then God let it rain’:

• Alors Dieu laissa pleuvoir.

• Alors Dieu fit en sorte qu’il pleuve or qu’il plût, or Dieu fit qu’il pleuve / qu’il plût, or Dieu fit pleuvoir.

More, this is stylistic because fire doesn’t rain, normally !