Does this mean I have an interview?
 

The woman asked me if I had any questions about the position, and I e-mailed back with a couple, saying that I would ask the others if and when there was an interview, to which she responded something along the lines of I do look forward to speaking with you soon.

Should I take this as having an interview, and can I ask to set up an appointment?

No, I don't believe that's saying that you have an interview definitely yet. You may have one in the future, or maybe a phone interview, but I do not see that as grounds to say hey, you said I can have an interview, let's set up a time. You COULD say, I would really like to set up an appointment to speak with you face to face, and do it that way, but never assume :)

Exactly - don't read into anything unless she explicitly tells you that you have an interview.

That seems like kind of a cruel thing to say, then... I mean, I basically was fishing to see if I had an interview, to which her response was that she looks forward to talking to me. I mean, if she were looking forward to talking to me to reject me, well, she's just a big meanie. :-P

I think it sounds promising. But she can probably not promise an interview until she's gone over everyone's applications, etc.

I'd say something like that to give a hint that you were one of my top choices.

She may not have the authority to make a decision on who is interviewed. She may not have the authority to begin interviewing anybody. She may not want to interview you and was trying to be polite in response to your nudging. The job hunting game sucks, but unfortunately right now the ball is in the employer's corner.