I'm re-watching Dark Matter (before I see Season 2) so this answer will be added to as I go along.
As <PERSON> said, in episode 4, <PERSON> killed several Casino employees in front of <PERSON>. <PERSON> was naturally very shocked (she flinched away from Two, stammering "Y-y-y-you-you kill..." before <PERSON> grabbed her by the arm and dragged her out of the casino basement).
At the end of the episode, Two wanted to talk to <PERSON> about the incident but <PERSON> didn't want to talk about it and left the room when <PERSON> insisted they discuss it.
This would be the point at which <PERSON> stopped trusting Two. Further incidents are given below, to show how the trust between <PERSON> and Two fluctuates.
In episode 5, <PERSON> asks the <PERSON> to keep the card she found a secret.
<PERSON>: Do me a favor, don't tell any of the others about this, okay?
<PERSON>: I thought you had resolved to trust them. Well, some of them anyway.
<PERSON>: Yeah, so did I.
However later in the episode Five states that she doesn't want Two (and One and Three) to die, so although she may not trust Two completely, she doesn't consider Two to be such an untrustworthy person that she deserves to die.
When Two brings up the casino incident later on in this episode, she states that she didn't mean to kill the men.
Two: Look, about what happened on the space station I'm sorry you had to see that. I didn't mean to kill those men. It was just...
Five: Instinct?
Two: I was going to say reflex. I wasn't ready, I wasn't in control. 865
Next time it'll be different.
So <PERSON> is trying to tell <PERSON> that she is trustworthy, and I think that at this point <PERSON> may trust <PERSON> a bit more than she did immediately after the casino incident but not enough to reveal any major secrets.
In episode 6, before <PERSON> dives into the memories, Two is very concerned and tries to stop her. Eventually, <PERSON> gives in but still provides reassurance to <PERSON>.
We'll be monitoring your vital signs. If anything goes wrong, we'll pull you out
Two holds <PERSON>'s hand tightly
Later on, when <PERSON> gets pulled out, she asks why and Two responds (vehemently):
Because I don't want you to have a stroke, that's why. Hey, this was a bad idea. **
Later on, Two and One volunteer to help Five but Six overrules them and goes to rescue her. At the end of the episode, they have this conversation:
Five: You know, it's one of the reasons why I didn't want to come back. I never felt like I knew who to trust out here. I mean, I thought I could trust Two, but sometimes she scares me a little.
Six: Yeah, join the club.
Five: But now, at least, I know I can trust you.
So it looks as though at this point, Five trusts <PERSON> a bit more than she did in episode 5, but still isn't sure about it.
More to come...
**In his response to this question <PERSON> says that "Both occasions revealed the "true" nature of <PERSON>'s character: a dangerous murderer." However her actions here show that <PERSON> is not (at the core) a bad person. 86