Q3:
C. Give her ceftriaxone 250mg IM once, followed by doxycycline 100mg and metronidazole 500mg twice daily for 14 days to take at home.
This is an effective outpatient regimen, and it is particularly appealing because it begins with a parenteral dose of a relatively long-acting beta-lactam antibiotic to which N. gonorrhoeae is reliably susceptible. Do not forget to ask about beta-lactam allergy. Her record should tell you what she was treated with, and tolerated, in the past.
There is an alternative regimen listed here that would also be appropriate. Have you found it?