Learn Italian: La natalità scende, il che aumenta l'immigrazione straniera. - The birth rate drops, which increases foreign immigration.

Normally, che (meaning "that" or "who") refers back to a specific noun. However, in this sentence, "which" doesn't refer to a single noun like "birth rate"—it refers to the entire preceding situation ("the birth rate drops"). Whenever "which" refers to a whole statement or fact, you must use il che.

Could I use la quale instead of il che since la natalità is feminine?

No. If you used la quale, it would strictly refer back to the feminine noun la natalità, changing the meaning to: "The birth rate drops, and the birth rate increases foreign immigration." Because we want to say that the drop itself causes the increase, we need the neutral phrase il che to point back to the whole idea.

Can aumentare (to increase) take a direct object like it does here?

Yes! Aumentare is a flexible verb. It can be intransitive (happening on its own), like "prices increase" (i prezzi aumentano). It can also be transitive (acting on something else), as it is here, where the situation (il che) actively increases a direct object (l'immigrazione).

Is scendere the usual verb for talking about dropping statistics?