Learn Portuguese (Portugal): Foi a médica quem te recomendou aplicar este sérum? - Was it the doctor f who recommended you to apply this serum?

It adds emphasis! Using Foi (It was) followed by quem (who) creates what is called a cleft sentence. It intensifies the focus on the subject (a médica) to clarify exactly who did the action. It is the Portuguese equivalent of asking "Was it the doctor who...?" rather than just "Did the doctor...?".

Could I use que instead of quem here, since it translates to "who" or "that"?

Yes, you could say Foi a médica que te recomendou..., and it is very common. However, when emphasizing a specific person in this type of structure, using quem is highly natural in Portugal and adds a slightly stronger, more precise focus on the identity of the person. Keep in mind that if the subject were an object rather than a person, you would have to use que.

Why is the pronoun te placed before the verb (te recomendou) instead of after it (recomendou-te)?

The word quem acts as a "magnet" for pronouns. Because quem is a relative pronoun, it forces the object pronoun (te) to move before the conjugated verb (a rule known as proclisis). If you didn't have the emphatic Foi... quem structure, the sentence would start with the subject and require a hyphen: A médica recomendou-te....

Why is aplicar in the infinitive here? Doesn't the verb recomendar usually trigger the subjunctive?