How do I get over these (possibly sexist) feelings regarding an underqualified labmate?
It seems as if you have two major issues.
1) This person doesn't know how to code
2) This person asks a lot of questions.

First, it would benefit you to remember that there are many skills required to be a good researcher. Examples include the ability to come up with good research problems, to develop theory, to read results in a way that makes connections/insights. This person may have been admitted because they are highly skilled at one of these other areas. The committee may believe that the person can pick up on the skills they lack. I myself started my PhD with horrendous gaps in my knowledge (my friends tell me that they were horrified by the questions I asked first year), but my letter writers were able to assure the committee that I was a quick study (and I was).

Second, you should remember that learning styles vary, and some people learn best by asking questions. It may not be your learning style, but one of the reasons study groups exist is that many people learn well by walking through problems and questions with others. This is the sort of thing that the askees seem to either love or hate. I had faculty tell me that I was their favorite student because I asked great clarifying questions during their courses/departmental seminars. I had other faculty tell me that I would never succeed in academia because "no one likes people who ask questions." If you are in group two, the best thing you can do is put in some headphones so you don't appear to be available for questions.