1. Yes, only Juarez issues those types of visas.
2. No. A civil surgeon is used in the US. Panel physicians conduct the visa medical exams in the foreign countries. There are only 2 medical clinics to use. They are in Juarez near the consulate.
3. You do not make an appointment. You show up early in the morning and wait in line. You will return later that afternoon to pick up your sealed up envelope with the results that you will take to your interview.
Here is how it works for Juarez:
You need to get your CDJ case #, invoice # and beneficiary ID # from the NVC before you can fill out the DS-260 by calling 603-334-0700
Juarez will send the USC and the beneficiary in Mexico a letter. Sometimes the letter does not reach the person in Mexico because of the crappy mail system there. If the only one that receives it is the USC, it can be mailed or scanned and emailed and printed out by the beneficiary in Mexico. It does not have to be the original.
The letter you receive points you to the sites where the instructions, forms and place to schedule your appointment and interview is. The letter is the only 'packet' you will receive. You should go to the links(which I am posting below) listed in the letter. The letter will be needed by the K-1 applicant at their ASC, medical and interview in Juarez, along with the confirmation page from the DS-260.
Here are the forms: http://ciudadjuarez.usconsulate.gov/fianceforms.html
instructions (very important to follow and they explain a lot): http://photos.state.gov/libraries/ciudadjuarez/231771/PDFs/packetk1may.pdf
schedule ASC: http://mexico.usvisa-info.com
and CDJ info: http://www.visajourney.com/consulates/index.php?ctry=Mexico&cty=Juarez
While waiting, you can read through the reviews to see how the procedure works and what documents were needed by others applying for a K-1: http://www.visajourney.com/reviews/index.php?cnty=Mexico&cty=&dfilter=5
Is getting married in the US important to you? Because a spousal visa is more elegant and cheaper and the immigrant can work right away, whereas with the K-1 visa the immigrant can't work for at least 3 months. You could get married now (anywhere in the world) and then chase a spousal visa. Something to consider.
It's fine that the USC lives abroad, but she will need a co-sponsor based in the US and might have to show her concrete plans to move back to the US.
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