So like Did they ever fully explain how the whole Darkspawn and Golden City thing actually went down?
Yes, but also no.
The Golden City: Elven god's (
Evanuris) palace. No mention of who or what the Maker is. The Veil Jumpers seem to jump that the Chantry lied (it usually does) and that the Maker is not real (Solas seemed to think so in DAI).
The elves were originally spirits that wanted to become flesh so used lyrium to become elves, while basing their forms on humans. Then the elves and Titans went to war as the elves wanted more lyrium (Titan's blood). Solas ended the war by creating and using the Rite of Tranquility on the Titans, accidentally creating the blight from the Titan's loss of dreaming. Solas then placed the blight into the Black City to keep it from infecting anyone.
The Golden City does not seem to be real. There is only the Black City.
The Evanuris then used the blight as a super weapon (for some reason) against Solas' rebellion, the Forgotten Ones and maybe the Executors. It do not work out and most of the Evanuris seemingly got infected with the blight.
The Evanuris were trapped in Veil by Solas because they kept being retards playing with the blight and for killing Mythal when she tried to stop them.
Mythal became shattered after being killed (because spirits and demons shatter instead) and some of her essence landed on women throughout DA history like Flemeth, Morrigan,
Andraste.
Yes, Andraste was a persona for an Mythal and most of the Veil Jumpers and the game do not seem too interested to look into the implications of what this means.
The Evanuris pretended to be the Old Gods (again for some reason) to gaslight the Ancient Tevinter Imperium Magisters to open up their prison in the Black City. It did not work. This is how the First Blight started, or at least how the magisters like Corypheus came to be. The Old Gods are sort of implied to be real also, just that the Evanuris somehow hijacked their connection to talk to the magisters.
Archdemons are phylacteries for the Evanuris so for each Archdemon killed, a Evanuris lost their life. Now they are only two Evanuris left: Elgar'nan and Ghilan'nain. Elgar'nan's Old God name was not Dumat, it was Lusacan interestingly enough. Why the Evanuris use High Dragons as furry personas is not really explained well other than dragons are magical.
Where darkspawn come from is sort of answered. It is just that the game is not really interested in following through. Like how come the Evanuris do not revive like Corypheus does? Or why use the blight as a weapon at all? What about broodmothers and awakened darkspawn? Where do the Titans come in, how are the involved? Why are the Evanuris commanding the Venatori instead of the Dalish elves that worship them?
TL;DR: Yes they do answer these questions. No, they do not really get into what really went happened with the Golden City or darkspawn. Only how it relates to how Evanuris did everything wrong and how Solas is a goodish guy.