How could a civilization that has not discovered electricity yet reliably mass produce aluminum and what uses would such a civilization have for it?
I will only address the first part of the question.
The most natural solution would be: the planet has minerals which contain aluminium in native or very reduced form.
On Earth and actually everywhere in the solar system aluminium occurs as aluminium oxide. Most of it is incorporated in plagioclase and clay minerals. Native aluminium exists as an extremely rare trace mineral in mantle rocks, often alloyed with iron and with traces of silicon and magnesium or - in meteorites - copper and zinc.
When a planet forms, the aluminium will always get oxidized. To get native aluminium there must be geological processes that produce it. You need a very reducing environment (low oxygen abundance) and high tmperatures (2000°C or so), so the planet should have high volcanic activity. Higher than terrestrial abundance of radioactive elements would help creating a higher temperature gradient and more volcanism. Native aluminium will form in the mantle, which is more reducing than crustal rocks, and will be transported to the surface by plate tectonics.
Conditions should be dry, at least locally, to prevent the aluminium from reacting with water in geological time scales.
High carbon abundance would facilitate the formation of native aluminium by carbothermic reactions like Al2O3 + 3 C -> 2 Al + 3 CO at temperatures above 1800°C. The process could also produce aluminium carbide (Al4C3). That would be a mineral from which aluminium metal would be relatively easy to recover (decomposition temperature 1400°C), but would again need very dry and reducing conditions to be stable. Even the presence of silicate would make the mineral unstable, leading to formation of aluminium oxide and silicon carbide (SiC).
Naturally, a planet that possesses appreciable amounts of native aluminium would have to have a large amount of other reduced minerals, too: elemental silicon, silicon carbide, native iron etc., all continuously produced by subterranean smelting processes and then brought to the surface where after some time they get oxidized by water and air. It would be a society with a generally better availability of industrially important elements than we have.