Jane Gates's Links
Jane at first sees Alex as another person to fool, much like she does with Engou. But as she realizes that she work together with him -- that they can do murders and get away with it -- she puts a degree of trust with Alex when playing DRcade with him.
However, by the end, when she's forced to always lie...not only does she recognize that Alex can see through her words, but that in truth, she wanted to speak her mind. Post game, she wonders just what sort of person Alex was irl, and considers him her one true friend.
After seeing Cal emerge from underground, she knew that she had to talk to her -- and understandably, threw Caliber in a loop. After a small exchange, Jane confidently decides that, true to her title, she needs to be able to give proper tours to the underground -- and Cal's going to help her, no matter the cost.
As a person, Jane finds Cal cool, and wants to gain power of her own. Eventually she does through a persona of her own (as well as a general friendship with some of the other slimes in the Labyrinths), and constantly contests her to improve her fighting prowess. However, she is still guarded about her -- not because she's a slime, but her trouble putting her full trust in others.
Jane was the first person that Cal came in contact with, for better or worse. After telling her about the Labyrinths, the two make a promise to exchange information -- with Cal's goal to learn as much as possible about the world for her own personal interest.
Despite how much Jane tries to fool Cal, she can read through her lies easily -- ironically, she's poor at social cues otherwise. She also cannot understand why Jane has zero fears about her despite her origins.