How can one go through Basic Training and Tech School, get promoted to A1C, receive three (3) Service Medals, and get an Honorable Discharge?

Well, the ribbons are (from left to right in the photo) National Defense Service Medal (NDM), Global War on Terrorism Service (GWOT-S), and BMT Graduation Ribbon.
BMT Grad & NDM are awarded upon graduation of BMT. Since she served during the designated time period provided for awarding of the Medal, she received it. Per AFPC's own website:
"Personnel supporting the Global War on Terrorism in a non-deployed status, whether stationed at home or overseas are eligible for the GWOT-S. Examples of this support include: maintaining/loading weapons systems for combat missions, securing installations against terrorism, augmenting command posts or crisis action teams, and processing personnel for deployment in support of the Global War on Terrorism."

I have a friend in my unit that came back from BMT with 4 ribbons: NDM, Marksman, BMT Honor Grad, & BMT Graduation.

She was there for 5 months. I would gather it was a medical discharge. Why the concern?

Entry level separation, it's probably a medical issue such as stress fractures or an injury sustained during training. It looks like she was separated in A school or just after.