I wonder if this means going forward there will also be a golden mole hidden in each image.
No, they only appear (and not so hidden) in the next image afterwards.
The only "easter eggs" hidden in Zookeepers pictures will remain the (violent) duck, a doughnut stamp (a.k.a Donut boy) and sometimes (but not always) a seal handpuppet.
I'm still waiting for an official Romanization of these (rather androgynous but apparently female) characters' names. The website URL has it spelled as "Naruse Takuto" for the pinkish-haired one, but "ใฟใฏใ" is often Romanized as "Tact" or "Takt". I think the bluish-haired one is more certain to be Romanized as "Shiki".
Aoi and Rin may act distant but I don't think they dislike or even have any negative feelings for Sensei, it's just that they're so effing busy all the time they can barely interact with him like a normal student would