I love reading this thread!!
Here are my thoughts...
Time Travel Deal:
Richard did not recognize Sawyer at all last night, which makes sense-this is the first time they are seeing each other. However, in 2004 when Flight 815 crashes, all The Others know the names of the Losties - since Richard met Sawyer back in 1974, he would know his name still in 2004, and he could tell his people.
Sawyer and group, upon meeting Richard in 2004 would recognize him I would think, since they met him back in 1974. They wouldn't know any of the other Others, except
maybe Ben if he arrives.
Remember Ben being in the hatch in 2004? The Losties didn't know who he was (at least from what I can remember). I wonder if Sawyer's group in 1974/77 are going to see/meet young Ben and then years later he's in their hatch...they still might not recognize him since it's been 20+ years. But they would recognize his name when they heard it. When did they first get Ben's real name?
Amy & Horace's Baby:
Hmmm...my first guess would be Jacob....
And thanks for the reminder on who Horace is everyone!

I wonder if Oliva was ever his actual wife...
Bag Lady:
I was all psyched up for the scene and then let out a "Oh." when I saw her. Instantly DH says, "She's in another show....24!" (the one other show we are obsessed with!)
Charloette:
I think that really is her as a young girl, 3/4/5 years old. I think the birth date Ben had was wrong. Her mother took her away from island when she was young and they moved to England. Perhaps her mother also changed her birth date (not legally obviously), to hide her...
Did anyone catch what the people walking with Charloette looked like? Could you see faces at all? Remember we were wondering if she was possibly the Dharma Film Guy's daughter?
The Others:
I don't think they are nasty yet. They pulled a truce with Dharma, so that at least tells you they are reasonable. I think something crazy happens that makes them get nasty. Perhaps Ben's leadership?
Richard:
I think he's Jacob too.
Babies being born on the island:
My DH said he thinks right now, 1977, babies can be born on the island, but something tweaks out the island that causes the babies not to be born - possibly the chemical used in The Purge, or a disruption of some sort on the island. The difference with this baby and Danielle's is that Amy must have gotten pregnant on the island since we see her in 1974 not pregnant. Danielle arrived pregnant, same with Claire.
Speaking of the Purge, is that where this show is going now? Is this whole season a "do over"? The Losties are going to stop Ben and prevent him from killing the Dharma employees?
I don't think they can prevent him, "what's done is done" sort of thing.