Oh she was having the mayor's baby. The whole reason is it looked bad on his image. I assume he was married( we never see her tho- and the house is empty...). The thing I never understood was- her friend still worked for the mayor even tho she knew he killed her. Blows my mind, she never looked bothered until the end.

Ummm- after noticing her in the campaign photo, I believe  Ga Mo Tak  connected the dots.  I don't remember it being an Ah moment- very low key to keep the 15+ rating I'm guessing?!?. The goal was never to solve her murder but to prevent him from going to the Blue house. Which is why they don't go into details. 

No problem! it was easy to miss - they also never said the blood was from the dog, but that is what I'm guessing. too