Can a primary care doctor prescribe psychiatric meds?

Yes. Using medicines requires knowledge of doses, indications, adverse effects, and interactions with other medicines.
Yes. More antidepressant medications are prescribed by primary care physicians than by psychiatrists. Any licensed physician can prescribe any medication, with a few exceptions. Primary care physicians vary greatly in their comfort level and skill in prescribing such medications, especially when using lithium or antipsychotics.
Primary care. Sure they can. Main concerns over long-term continued prescribing is side-effects & possible liability issue.