Will a walk in clinic with primary care services give anti-depressants?

Not likely. Walk in clinics are generally set up to handle acute, "one time" episodes like strep throat, sinus infections, and utis as an example. Ideally, you want to find a good pcp or psychiatrist to spend the time with you to talk through your symptoms, possibly prescribe meds and be available for follow up. Check this app (healthtap) or healthgrades for a list of docs in your area. Take care.
Not likely. It's not likely. And i hope not! responsibly treating someone with anti-depressants requires first, a reliable diagnosis that is determined by a detailed history, and second, careful followup to be sure the medicine is working and evaluating that medicine for possible side effects. Most walk-in clinics don't have the time to do that. Their practice model is faster turnover.
Clinic. Not likely unless you are already on anti depressants and you ran out of the medication. The clinic will contact your physician and confirm.