So, Alessa split her soul (this is often seen in Japanese myths for some reason) and one half of her becomes Cheryl.
Harry Mason adopts Cheryl.
What was Alessa's astral projection doing in silent hill when Harry saw her?
Also, at the end of silent hill 1, does alessa become whole again?
How does that all tie up in SH3 with heather? Is heather a whole Alessa?

Cheryl wanted to go to Silent Hill because she was subconsciously attracted by Alessa's pain and an urge to reunite and help her, and Alessa's astral projection was there in order to unify with Cheryl. After the car crash, Cheryl's soul is already merged with Alessa's astral projection the entire game, and Alessa is attempting to complete a ritual that would allow her (and the God) to die. At the end, the two components Dahlia merges is the completed soul, and the body containing God.

The newborn baby that God hands Harry after the boss fight is, indeed, Heather, who is the reincarnated complete soul. Heather therefore starts recovering the memories of both Alessa and Cheryl over the course of SH3.

I see, thanks a lot