1 ) I think that if Karen hadn't decided to remain close enough for Dorothy to access (but not do anything to encounter her), she would have still had trouble accepting why she would have left her behind, but she would have been able to move on from it and accept that there was a reason she'd had to leave her with the Gales. Little is shown besides Karen leaving her with the Gales and Dorothy and Em having a brief discussion about it, but she mentions that Karen hasn't reached out and that she ends up making the drive to Karen's trailer often enough for Em to comment on it, which suggests she's been trying to work up the courage to reach out on her own for quite a while. I think that while good-intentioned, Karen's choice to remain close but not accessible left Dorothy feeling unwanted and with deep-seeded self-esteem issues in spite of the life she's built for herself as a skilled young nurse and a devoted daughter ('I wished I was more').
2 ) I think that while realizing she was capable of cruelty like that frightened her and she'd be scared to access the part of herself that's comfortable with performing them, especially on people she'd loved, she does feel that she was justified in doing what she'd done (which is something she feels equally as frightened and conflicted about). She'd want to enact them only as a last resort, which falls in line with other violent acts she commits against others (as another example, tricking the witch of the East into using the gun on herself when she had her and Lucas imprisoned) and she would never want to feel comfortable enacting them, but she would enact them.
If she'd been able to knock him out without resorting to hanging him on the cross she'd still need to leave him behind (the real thing that horrifies her is how she left him in the same exact state she'd found him in, something that when she'd found him had seemed like an unimaginably cruel way to punish someone), but given that he ends up finding her at home at the end of the series, presumably to bring her back to work with him, I imagine it would take a lot of work on both their parts to end up trusting each other and feeling safe enough to work together again. I think his desire to change and make things right, not only with her but with the people he'd harmed while working under Glinda and the Wizard, would go a long way in her trusting him again. Her hesitation to kill him comes from what she'd seen of that in the time she'd known him and the knowledge that he hadn't had a choice in turning on her since he'd been under Glinda's influence.
3 ) While frustrated that she'd be pulled into another world again, she's at least familiar with the concept of needing to learn how a new world works and could probably help those less familiar with it to cope. I'm sure that the bonds she'd form with people would help her find the bright in the situation and she'd be willing to assist in missions and protecting people. The desire to go back home could still potentially get her in trouble (I could see her becoming reckless in exploration in trying to find some sort of method to get back home), but knowing she's not the only displaced one would make her want to stay until others were able to find a way back too.
4 ) Upon the realization of how medicine works here she would still want to volunteer to worth within the first aid center (she'd also be among those who'd offer to patch people up for free). She may be suspicious of the pills and injections and want to know how they work, and I could see her trying to learn by asking other (human) medical professionals about what they contain and keeping a small stock of things like charcoal and honey if they're available for medical methods people might not be able to afford to go to the clinics or hospitals for (and possibly getting into trouble for both her curiosity and taking business from clinics).
addendum
2 ) I think that while realizing she was capable of cruelty like that frightened her and she'd be scared to access the part of herself that's comfortable with performing them, especially on people she'd loved, she does feel that she was justified in doing what she'd done (which is something she feels equally as frightened and conflicted about). She'd want to enact them only as a last resort, which falls in line with other violent acts she commits against others (as another example, tricking the witch of the East into using the gun on herself when she had her and Lucas imprisoned) and she would never want to feel comfortable enacting them, but she would enact them.
If she'd been able to knock him out without resorting to hanging him on the cross she'd still need to leave him behind (the real thing that horrifies her is how she left him in the same exact state she'd found him in, something that when she'd found him had seemed like an unimaginably cruel way to punish someone), but given that he ends up finding her at home at the end of the series, presumably to bring her back to work with him, I imagine it would take a lot of work on both their parts to end up trusting each other and feeling safe enough to work together again. I think his desire to change and make things right, not only with her but with the people he'd harmed while working under Glinda and the Wizard, would go a long way in her trusting him again. Her hesitation to kill him comes from what she'd seen of that in the time she'd known him and the knowledge that he hadn't had a choice in turning on her since he'd been under Glinda's influence.
3 ) While frustrated that she'd be pulled into another world again, she's at least familiar with the concept of needing to learn how a new world works and could probably help those less familiar with it to cope. I'm sure that the bonds she'd form with people would help her find the bright in the situation and she'd be willing to assist in missions and protecting people. The desire to go back home could still potentially get her in trouble (I could see her becoming reckless in exploration in trying to find some sort of method to get back home), but knowing she's not the only displaced one would make her want to stay until others were able to find a way back too.
4 ) Upon the realization of how medicine works here she would still want to volunteer to worth within the first aid center (she'd also be among those who'd offer to patch people up for free). She may be suspicious of the pills and injections and want to know how they work, and I could see her trying to learn by asking other (human) medical professionals about what they contain and keeping a small stock of things like charcoal and honey if they're available for medical methods people might not be able to afford to go to the clinics or hospitals for (and possibly getting into trouble for both her curiosity and taking business from clinics).