She waited by the creek even after the gun shot, but came running when she heard Sayid calling her?

LOL I thought that was odd too – it seems like once she heard the gunshots she either would have come to help them, or ran back to her home and hid.

I understand that Kate told Rousseau that she wants to find the Others’ camp on the main island, but I’m not convinced Kate expects to find Alex there. I was thinking she planned on threatening/blackmailing the Others on the main island into arranging for Jack to be released (although I’m sure it’s not a very well thought-out plan). She mentioned Alex to Rousseau primarily so Rousseau would agree to help her find the Others’ camp. Kate knows Jack was being held captive on the other island – I don’t think she’d expect that they would bring him back to the main island – the other island is a perfect prison, with little to no chance of escape. And if he’s there, they’d have to have guards there. When Kate and Sawyer left that island, Juliet told Alex she couldn’t go with them. And that all happened within the last couple days of island time. To me, all of this adds up to Kate assuming that Alex is still on the other island. However, I don’t think Kate has actually concerned herself with where Alex is, she’s focused on getting Jack back, and she doesn’t have any reason to believe he’s on the main island. (I realize this is not a very significant plot point – they will find what they find – I just wanted to explain my thinking)

As far as Rousseau being a plant/spy…I can’t completely rule that out, but to me it seems unlikely. If she was part of the Others, she would know about Alex, let alone be part of her life. And her actions/reactions all along have seemed genuine in that she wants to find her daughter (for example, her statement at the end of the “Maternity Leave” episode – “you are not the only one who didn’t find what they were looking for”). Also, in Maternity Leave, she seemed genuinely surprised to see the Medical Hatch. And all of the other things we’ve learned about her – booby traps she has set all over the island, her voice on the transmission that’s been playing for 16 years, her fortress where she took Sayid to after catching him – all of that makes me think she’s living independent of the Others. Like she said in Enter 77, she has survived for 16 years by NOT exploring too much (as opposed to Locke who has put his and other Losties lives at danger with his curiosity). Unless this is part of a very elaborate deception, which is possible and which is why I don’t completely rule out this plant/spy theory, I don’t think Rousseau is part of the Others.

unanswered questions now brought up from this theory:

how a presumably primitive indigenous people could become powerful enough to purge the well armed dharma folk from the island.

How the indigenous people would then get so completely immersed in present day american culture… even watching baseball games? i mean, yeah, they had the satellite capabilities, but it just doesn’t add up to me…

how they then gained the funding to not only find juliette before she ever published her research, but to also fund her ongoing research on infertility.

Maybe the indigenous people on the island are actually from the past and the future. They might be guardians to the fold into time that’s on the island(or whatever!) and so have access to all time. Maybe they know something about the future (the demise of the human race?) and so are the “good guys” because they’re trying to change the fate of mankind. Maybe fertility has something to do with it ala “Children of Men” or “Handmaiden’s Tale” where the human race can no longer reproduce. Kind of significant and maybe not so coincidental that both these hostiles and the Dharma Initiative are working along the same lines, and so for awhile they co-existed on the island. But something happened (the incident?) and they decided to purge.
So, the lady in the jewelry store was actually one of them, making sure Desmond was on the right path.
Still don’t know how the smoke monster would fit into all of this – unless he’s the advanced security system from the future helping to guard access to the time warp? Why he would have it out for Eko I don’t know!!

Regarding how Rousseau “knew” Alex wasn’t at the Flame Station – when Kate left Hydra island a day or two prior, Alex was still there. So as far as they (Kate and Rousseau) know, she’s still on that island, along with Jack.

I agree with Hammer….further supports a spy/plant theory.

I believe Kate/Locke/Sayid were going to the north side of the island based on Karl’s info about the Others living on THIS island.

When Desmond first surfaced on the island and Kelvin “found” him, weren’t there several people in yellow suits dragging him to the hatch? That seems to be my recollection. Who/where are the other people?

Why didn’t Rousseau think it was possible for Alex to be in the Flame? I don’t get why her first thought wasn’t “Alex could be here”.

Desmond vision was blurred and doubled, there was only
one person.

Rousseau IMO didn’t ask because she knew Alex wasn’t their. Further supports my theory that she is an other or has an aliance with the others.