Okay so after some extensive testing I think I have a near-complete list of all adoptable children. Here's the list and I'll give some explanation, findings, and caveats further down.
Hearthfire New NPC's Lucia / Whiterun / Beggar girl in Whiterun; kicked out by uncle and aunt. Sofie / Windhelm / Flower girl in Windhlem; father's a Stormcloak who died in battle. Aleson / Dawnstar / Boy; helps miners in Dawnstar. Blaise / Katla's Farm / Boy; parents in Legion died from ambush, works for Katla for a place to stay.
The Honorhall Original Four Samuel / Honorhall / Boy; never met his parents, wants a real family. Hroar / Honorhall / Boy; named after sound lions make, roarrrr. Francois Beaufort / Honorhall / Boy; parents left him at orphange a year ago, but disappeared since. Runa Fair-Shield / Honorhall / Only girl of the Original Four, gets picked on by the boys.
Conditional Adoptees Dorthe / Riverwood / Alvor and Sigrid's daughter; wants to grow up to be a blacksmith. Frodnar / Riverwood / Hod and Gerdur's son; enjoys playing pranks on others. Braith / Whiterun / Amren and Saffir's daughter; “What are you looking at? I'm not afraid of you you know? Even if you're my elder.” Britte / Rorikstead / Lemkil's abused daughter; bullies twin sister Sissel. Sissel / Rorikstead / Lemkil's abused daughter; Britte's meek twin sister. Gralnach / Heartwood Mill / Leifnarr and Grosta's son; maybe a glitch, but comes to orphanage with a sword on his back. Eirid / Winterhold / Dagur and Haran's daughter; plays the Elf in the “Hunt the Elf” game with Jarl's kid Assur. Knud / Katla's Farm / Son of Katla and Snilling at the farm. Svari / Solitude / Daughter of Addvar and Greta; uncle Roggvir executed in Solitude; one of three kids playing tag. Minette Vinius / Solitude / Daughter of inn owner Corpulus Vinius; said to be “greg-gare-ree-yus”; one of three kids playing tag. Kayd / Solitude / Son of Sayma and Beirand; one of three kids playing tag. Skuli / Old Hroldan Inn / Son of Eydis; mature for his age; actually hires Leontius Salvius to run inn; only moves if that guy's dead too. Erith / Left Hand Mine / Daughter of Daighre; has a dog Torom.
Unadoptables Mila Valentia / Whiterun / Unadoptable even if mother Carlotta is dead. Haming / Froki's Shack / Unadoptable boy who escaped Helgen at the beginning; lives with grandfather Froki. Adara / Markarth / Daugther of silversmiths Endon and Kerah; unadoptable because Endon is essential. Agni / Morthal / Orphan girl living with wizard Falion; unadoptable because she has no parents and Falion is essential. Virkmund / Morthal / Son of Thonnir and Laelette the Vampire; unadoptable since Thonnir is essnetial.
So basically there are four categories of adoptable kids. The first, the four new NPC's added as part of Hearthfire, can be adopted *unconditionally*. If you don't want to kill anyone at all, these are the only kids you can adopt.
The second, the Honorhall Original Four, can be adopted once you kill Grelod and you get the letter from Constance Michel.
The "conditional adoptees" are available for adoption once their parents are dead. After the death for their parents, the kids will actually move to the Honorhall Orphanage, *provided there is enough room there*.
In Honorhall there are 12 child-sized beds. 5 of them belong to the Original Four plus Aventus Aretino, and these beds are owned and cannot be used by others. The other 7 beds are inside the smaller room, and will be used by the newly orphaned kids who just arrived. Thus you can actually get into a situation where 11 kids are cramped inside of Honorhall. Sometimes they will head out and play in the backyard, but they seem to only do so in groups (the 4 together and the 7 together).
The final category are kids that can't be adopted, some even if their parents are dead.
Some fun facts: -Britte and Sissel have abusive father, so if you want to do the "kill parents to save kid" thing they are probably your best option.
-Britte and Sissel is also the only chance you have for adopting twins.
-If the Honorhall is full, and a new kid gets orphaned, they will simply stay and do whatever they normally do. E.g., those in Solitude will continue to play tag.
-Gralnach arrives at the Honorhall with a sword on his back in my game. Not sure if this is a glitch or not.
-To adopt Skuli, it's not enough to kill off his mother (father is already dead), you must kill Leontius Salvius too. Otherwise, Skuli will hire the guy to run his mother's inn.
-I didn't bother trying Jarls' kids, since the Jarls are essential.
-I also didn't try kids of clans, like Lars Battle-Born, because I'm not sure how many need to die. But there are probably some adoptable ones here.
-Among adoptable kids, Braith is a redguard, Francois Beaufort and Samuel are imperials, and Erith is a Breton. Every other adoptable child is a Nord. Actually, I'm not sure about the races of the new Hearthfire NPC's.
Now can someone please help me decide who to adopt? =( I have Sofie so far.