Learn Spanish (Spain): La directora, cuyo sector es difícil, ha adquirido el inmueble. - The director, whose sector is difficult, has acquired the property.

In Spanish, the relative adjective cuyo must agree in gender and number with the noun that comes after it (the thing possessed), not the person who owns it. Since sector is a masculine singular noun, you must use cuyo, even though it belongs to la directora.

Could I replace cuyo sector with el sector de la cual?

Grammatically you could say el sector de la cual to mean 'the sector of whom', but it sounds clunky and overly complicated here. Cuyo is the standard, natural way to express 'whose' when directly modifying a noun in this way.

Does the word inmueble mean the same thing as propiedad?

Yes, but inmueble is more specific. It refers strictly to real estate, like a building, land, or house (literally an immovable property). Propiedad can mean real estate, but it can also refer to ownership in general or any item someone owns.

Why use the present perfect ha adquirido instead of the simple past adquirió?

In Spain, the present perfect (ha adquirido) is used when an action happened very recently or in a timeframe still connected to the present, like 'this week'. If the purchase happened in a clearly finished past period, like 'last year', you would use the simple past adquirió.