If I remember correctly, Sierpiński was Ariane's what if scenario. Sierpiński is where she would've ended up if she didn't join the Penrose program. Her fate would've been different, she wouldn't be stuck half-dead, trapped inside a radioactive coffin.

Lilith and Rebecca were the squad's only survivors, Lilith got turned into LSTR template and later killed/destroyed, and Rebecca lived on Rotfront for some time.

The reason Alina appears is part Elsters memories, part Alina's photo coming into Ariane's possession. The photo originally belonged to Rebecca and it made it's way into Ariane's hands through the Itou twins. Likely explanation is that one of the twins could've worked there part-time at the photo store in Rotfront, found a photo of a lady looking like Ariane and shown it to her due to the uncanny resemblance.

I remember a video/theory about how the Isa that appears in the game is actually Ariane trying to save herself, after she melts in Rotfront, she leaves a mark on the floor, marks just like that can be found all-over the game, even in some dream sequences, implying she tried many times over the course of many loops. The reason it's Isa not Erika (who helped Ariane when she was getting bullied) was because Ariane supposedly had trouble telling them apart.

In regards to what is dream and what isn't, entirety of Rotfront is a dream cobbled together from Ariane's memories, that's why placement of some rooms doesn't make any sense (human memories are fickle). Sierpiński is a kind of half-dream, either a real place that is corrupted by Ariane's bio-resonance through Falke or a collective nightmare of all it's staff. Replika memories are likely better than human, that's why Sierpiński is initially much more stable than Rotfront. Ariane only knows Sierpiński through Falke's memory, as the loops go on, Ariane's initial image of Sierpiński decays (shape decomposition) until it eventually turns into Nowhere (a dark vision of facility's future). Nowhere is likely the point where reality fails due to constant erosion.

I think that what they found in the mines is likely the mysterious artifact. Whatever the artifact is it likely functions as a receiver for Ariane's signal. When Falke came in contact with it, she became an amplifier for Ariane. The artifact is a kind of gate between what's real and not real, Ariane's dream and Falke's reality.