Learn Swedish: Processen har utvecklats för att hjälpa personalen. - The process has been developed to help the staff.

The present perfect passive is formed by taking har plus the supinum form of the verb (the form you normally use after har) and adding an -s. The active supinum of utveckla (to develop) is utvecklat, so adding the passive -s gives us har utvecklats (has been developed).

Could I use har blivit instead to make this passive?

Yes, you could say har blivit utvecklad instead of har utvecklats. Both mean "has been developed." The s-passive is very common in formal, written, or professional contexts (like talking about a company process), while the blivit passive is often preferred in everyday speech.

Why is it för att hjälpa and not just att hjälpa?

In Swedish, when the English "to" means "in order to" (showing the purpose or goal of an action), you must use för att. If you only used att hjälpa, it wouldn't properly express the reason why the process was developed.

Is personalen treated as singular or plural here?

Personalen is a grammatically singular word (an en-word in its definite form: en personal becomes personalen), even though it refers to a group of people. It works just like the English collective noun "the staff".