Yes, "Praxis" is only used for referring to the offices of doctors, dentists, therapists i.e. everything to do with practicioners of medicine. The full translation of doctor's office is "Arztpraxis", but you can just use Praxis. There are other special words for offices, such as "Kanzlei" or "Anwaltskanzlei" for the offices of lawyers.
There's a little bit of difference between a clinic and a doctor's office(/practice/surgery). Clinics are more of a group thing--rather than being specific to one particular physician--and may not have a doctor at all (e.g., a clinic in a high school).
Yes, sabrinaritter and Phil821335 are right. British English uses surgery to mean 'a place of practice for a professional'. Or as I like think of it: 'a place for normal people to meet a person-of-status'. So, your doctor has a surgery and so does the local politician.
Duolingo uses almost completely US English, but the Brit. English alternatives should be acceptable options. And so it seems to be with this one as well. It accepts 'She is seldom in the surgery'.
"Hardly" relates to the degree or extent of something: Barely, only just, almost not. (See https://en.wiktionary.org/wiki/hardly#Adverb)
"Rarely" has more to do with frequency. See https://en.wiktionary.org/wiki/rarely#Adverb.
It certain circumstances--especially when paired with a temporal word like "ever"--it may be a subtle difference, but there is a difference. Think of the root words and answer this:
Would you rather have a rare steak or a hard steak?
"Rare" is an adjective. You need an adverb, because you're not modifying "she", you're modifying "in the office" or "in the practice". "Rarely" should work.
"In the practice" should be okay, assuming you're talking about a doctor who doesn't spend a lot of time in her own practice. "Doctor's office" makes it sound as though you're talking about a patient, or someone else to whom the office does not belong.