You have asked some good general questions, here, SAH. But, within this, I have to ask - or rather, I think YOU have to ask yourself - if you may be judging her too harshly. Pirkei Avot states that one should not judge others until you have reached their position. I don't know if that adage applies to non-Jews, halachically. Even if not, I would venture that this is a common ethical behavior for humanity.
I can't evaluate what factors went into your judgement of "bad middos" as a Gentile. Perhaps, you viewed her by your own "higher" ethical standards - meaning by your personal behavior. Did you expect her to live up to your standards, or common Jewish standards? Either way, she was a Gentile, so that may have been an unfair judgement.
OK, now she converted. I don't know what her motives were, but, yes, she is expected to live up to a different standard than when she was Gentile. But even within Judaism, there is a huge gamut of what is considered "good middos". It may not be your personal standard, but it may be acceptable.
Even if not, I think you need to keep that Pirkei Avot adage in mind, esp. now that she is a fellow Jew. Converts frequently undergo "post Judaic" stress. Suddenly they realize that being Jewish is far more challenging than they thought. Maybe your friend realizes that she made a mistake, but she can't reverse, now. This could be quite traumatic for her.
I think a good (not necessarily the BEST) option is to be a true caring friend, if you want to deal with this person at all. Ask questions to discover her challenges and problems in the process of conversion as well as now. Get a sense of what her position is before you judge her. If you can be helpful, wonderful. If you can't, refer her to someone who can. You're not obligated to shoulder the burden of the solution on your own. But, I think the proper "Jewish" behavior is to at least offer a caring shoulder and not be quick to judge others.