Is it unprofessional my company is asking me to interview someone applying for a position identical to mine, but in a different district?

No, why would it be unprofessional? They want someone who knows just what the job really requires to help evaluate the candidates.

Not at all, you are the best person that knows what your job involves, and at the same time you are gaining interviewing experience, in my opinion, its quite a compliment to you. I would ask the interviewee some testing question about situation you have faced and they may have to consider. Make sure you ask difficult questions and remember to to keep note of the answers as you may be asked to give feedback

not at all, you are the best person to know the ins and out of your work profile .

Also your company might be judging your capability, by making you interview this person

It's not unprofessional at all. Quite the opposite. Hiring is incredibly important and your company thinks highly enough of you to want you to be part of that process.

No...it is an indiction that they think you know about the job you do and that you have had relevant interview training, so are likely to be able to choose the right candidate

I'm a RN. Every time I've interviewed for a job, the interviewers have been the nurses I'd be working with.

Not at all. Its actually incredibly common, and should be somewhat flattering.

What it means is that the company value and appreciate that you are good at your job, and want you to conduct an interview so that you can find them someone else just like you. They are showing here that they think you're the expect in your job, and want your input on other people doing the job.

I don't know about unprofessional, but it is suspicious. Unless it is a compliment to you