Prima should agree with lucis: primae.Aurora, lady of first light, my lady; I implore you.
Aurora, domina lucis prima, domina mea; obsecro te.
Artifex doesn't really mean "master", but more like "artificer" or "maker".Apollo, lord of the sun, master of music, my lord; I implore you
Apollo, domine solis, artifex musicae, domine mi, obsecro te.
"Vulcan" in Latin is Volcanus, i (or, alternatively, Vulcanus, i). Vocative in -e, as is regular for that declension.Vulcan, lord of fire, divine smith, my lord; I implore you.
Vulcan, domine ignis, faber divine, domine mi; obsecro te.
Since Hades is taken from Greek, perhaps it should take a Greek vocative, Hade. Or you could use his other name, which is more usually found in Latin, Pluto.Hades, wealthy father, the unseen one, my lord; I implore you
Hades, Dis Pater, une inaspectus, domine mi; obsecro te.
Mercury in Latin is Mercurius, i (vocative Mercuri).Mercury, swift foot, divine messenger, my lord; I implore you.
Mercury, pes celer, nunti divine, domine mi; obsecro te.
Maybe it would be good to say Tellus Mater, to avoid repeating Terra.Terra, mother earth, my lady; I implore you.
Terra, Terra Mater, domina mea; obsecro te.
Same here as above concerning Hades.Hades, Wealthy Father, King of the dead; my lord, I implore you. Hades, Dis Pater, Rex mortui, domine mi, obsecro te.
Erebus is in the wrong case (it should be vocative).Erebus, Pater umbrae, Domine tenebrae; domine mi, obsecro te.
Erebus, Father of the shadows, Lord of darkness; my lord, I implore you.
I think the word you had first used for "unseen" was better than this one.Hade, Dis Pater,invisitate, domine mi; obsecro te.
The vocative of Erebus is Erebe, not Erebi. It's nouns that end in -ius in the nominative that end in -i in the vocative.Erebi, Pater umbrarum, Domine tenebrarum; domine mi, obsecro te
It's also found in the other order.I would make it primae lucis instead of other way around, because that (prima lux) is a very common way of saying daybreak.