"Elle fait semblant de boire."
Is semblant a noun or an adjective here?
There is no adjective semblant although it existed as such in old French.
Here, semblant is part of the idiom faire semblant which means "to simulate", "pretend", "feign".
Semblant alone is the participe présent (present participle) of the verb sembler or the noun derived from it.
Semblant is the present continuous form of the verb sembler. The usual adjective would be semblable. The present continuous form can be substantivised, as in le prétendant (and indeed, le semblant) and it can be adjectival, café chantant, place payante...
Idiomatic constructions with faire can take either a noun or an adjective, as in faire le con (noun, as evident from le), faire partie (noun, even though there is no article present) cela fait drôle (adjective, but idioms in the class are viewed as low-brow); cela fait chic
On fait semblant de chanter, for instance. This de might make one lean toward semblant being adjectival in this context, as we also say things like cela fait chic d'arriver légèrement en retard.