Learn Hardcore Portuguese (Portugal): Conheço a médica cuja consulta foi remarcada para amanhã. - I know the doctor whose appointment was rescheduled for tomorrow.

Because cujo/cuja/cujos/cujas is the relative pronoun used to express possession, equivalent to English whose. It links two nouns by an “of” relationship: here, consulta (appointment) belongs to the doctor. The simpler relative que cannot express possession. If you avoid cuja, you must rephrase:

Conheço a médica; a consulta com ela foi remarcada para amanhã.
Conheço a médica com quem remarcaram a consulta para amanhã.

Which noun determines the form of cuja?

The possessed noun does. Here it’s consulta (feminine singular), so we use cuja. Forms:

Masculine singular: cujo (o médico cujo consultório…)
Feminine singular: cuja (a médica cuja consulta…)
Masculine plural: cujos (o médico cujos horários…)
Feminine plural: cujas (a médica cujas consultas…)

Can I say cuja a consulta or de cuja consulta?

No. You must not use an article after cujo/cuja, and you must not put de before it because cujo already encodes the idea of de (“of”). Correct: cuja consulta. Note: other prepositions can precede cujo when required by the verb/noun, e.g. a cuja casa fui (I went to whose house), com cuja ajuda (with whose help).

Is cuja common in everyday European Portuguese?

It’s fine and clear, but sounds a bit formal. Very natural alternatives while keeping the meaning “the appointment with her”:

Conheço a médica; a consulta com ela foi remarcada para amanhã.
Conheço a médica com quem remarcaram a consulta para amanhã.
Conheço a médica; remarcaram a consulta com ela para amanhã.

Does cuja here mean “the doctor’s own appointment” or “the appointment with that doctor”?

In this context it’s best read as “the appointment with that doctor.” In Portuguese, saying a consulta da médica naturally means “the consultation with that doctor.” If you wanted to avoid any ambiguity, use one of the “com ela/com quem” rephrasings above.

Why is it a médica and not o médico?

Because médica is the feminine form of médico, indicating a female doctor. Many professions have distinct masculine/feminine forms (médico/médica, enfermeiro/enfermeira).

Could I use uma médica instead of a médica?

a médica = the specific doctor already identifiable in context (definite).
uma médica = some doctor, not a specific one (indefinite). Here, the sentence points to a specific person, so a médica is appropriate.

Is the a before médica the “personal a” like in Spanish?

No. Portuguese does not have the Spanish-style “personal a.” The a here is simply the definite article “the.”

Why is it Conheço and not Sei?

Portuguese distinguishes:

conhecer = to be acquainted/familiar with people, places, works (Conheço a médica).
saber = to know facts or how to do something (Sei a resposta; Sei falar português). So you say Conheço a médica, not Sei a médica.

What does consulta mean here? Is it “consultation” or “appointment”?

In Portugal, consulta commonly means a medical appointment. Useful verbs:

marcar uma consulta = to schedule an appointment
desmarcar a consulta = to cancel the appointment
remarcar a consulta = to reschedule the appointment
adiar a consulta = to postpone the appointment (usually to a later date)

Why foi remarcada and not está remarcada?

foi remarcada (ser + past participle) = passive voice focusing on the event: it was rescheduled.
está remarcada (estar + past participle) = focuses on the resulting state: it is (now) rescheduled. Both can work; the original emphasizes the rescheduling action.

Who did the rescheduling? How would I say it?

The agent is unspecified. To add it, use por:

A consulta foi remarcada para amanhã pela clínica.
A consulta foi remarcada para amanhã pela rececionista.

Why para amanhã and not em amanhã or a amanhã?

For scheduled times/destinations, Portuguese uses para: remarcar para amanhã. You don’t use em or a here. Also, amanhã is an adverb, so no article is used.

Does remarcada agree with consulta?

Yes. In the passive, the past participle agrees in gender and number with the subject. A consulta is feminine singular, so remarcada. Plural would be remarcadas.

Could I say “foi marcada” instead of “foi remarcada”?

foi marcada = was scheduled (the first time).
foi remarcada = was rescheduled (changed to a new time). Use remarcada to show it was moved from a previous time.

Can I drop the subject pronoun eu before conheço?

Yes. Portuguese is a pro-drop language. Conheço already encodes “I know.” You can say Eu conheço for emphasis, but it’s not required.

Any pronunciation tips for this sentence in European Portuguese?

conheço: nh = “ny” (con-YEH-soo); ç = “s”
médica: open É; final -a reduces (MÉ-dik-ɐ)
cuja: j = “zh” (KOO-zhɐ)
consulta: first o is nasal (kõ-SUL-tɐ)
foi: “foy”
remarcada: initial r is throaty [ʁ] (ʁɨ-mar-KA-dɐ)
para: PA-rɐ
amanhã: nasal ã and nh (ɐ-mɐ-NYÃ)