Q: Where did Moeka work part-time?
A: She worked at an editorial company called ArcRewrite. She quits after 2-3 days. In the δ world line (from Hiyokurenri no Da-rin) she continues working at ArcRewrite.
Q: Why doesn’t Moeka remember herself from the other world line like Rukako and Feiris did?
A: It is unknown why Rukako and Feiris were able to remember themselves in another world line. It is said that everybody has the Reading Steiner ability and it’s strength is different for each person. Moeka’s reading steiner was just weak.
Q:Moeka was able to dodge Suzuha’s bullet and disable her pistol out of her hand, so why didn’t she have the strength to fight off Okabe?
A:In the original game there was no depiction of Moeka being super human or having any sort of strength. Moeka kicking the gun out of Suzuha’s hand was just added in the anime version to bring more action into the scene.
http://www45.atwiki.jp/stein_sgate/pages/62.html
Q: How are Okabe and Moeka related in this episode’s world line?
A: Since Moeka was able to obtain the IBN5100, she has only met Okabe once and never visited the lab, nor has she met Mayuri. 
Timeline
July 29: Moeka meets Okabe and asks about the IBN5100. Hearing from Daru Okabe tells her it’s rare.
July 30: Okabe reads John Titor’s post on the message board, “the IBN5100 is needed to change the future”
July 31: Moeka receives a d-mail from her future self telling her the whereabouts of the IBN5100. Moeka reports to FB, steals it from the shrine, and stores it inside a coin locker.
July 31: Okabe finds out he needs the IBN5100 to decode the database found when hacking SERN.
July 31: Okabe finds out the IBN5100 is stolen from the shrine.
August 03: Moeka stops all contact with Okabe after she completes her mission (obtaining the IBN5100), she never meets Mayuri either.
August 11:Moeka starts to lose her mind after FB stops responding to her mails (Okabe time leaps and enters her room)
August 15: Moeka commits suicide in her room
August 16: Okabe hears from the police that Moeka has committed suicide. Mayuri dies at the comic market. Okabe time leaps back in time to August 11.
Q:Why doesn’t Okabe alert himself to obtain the IBN5100 using the d-mail before Moeka receiver her d-mail on July 31st?
A: Okabe realizes due to the butterfly effect, sending another d-mail might cause unintended consequences, so he decides and takes the safest measure which is to cancel out Moeka’s d-mail. 
Q: Why doesn’t Okabe send a d-mail warning himself to not let anyone use the d-mail?
A: In the current world line (0.52%) Moeka has received a d-mail from herself to obtain the IBN5100. She no longer needs to use a d-mail in the current world line. This means even if Okabe were to receive a d-mail in the current world line to stop her from using it, Moeka would never be there to use it in the first place.
The same could be said with Feiris and Rukako:
Feiris ~ She exists in a world line where her father is alive, therefore she no longer needs to use a d-mail to bring her father back to life.
Ruka ~ Ruka is born as a girl, therefore she has no need to use the d-mail to change himself into a girl.
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