Learn Russian: Этот проект касался статуса всей команды. - This project concerned the status of the whole team.

The verb касаться (to touch upon, to concern) requires its object to be in the Genitive case, not the Accusative. This verb falls into the same advanced category of verbs you are learning now that govern the Genitive for abstract concepts, similar to verbs of seeking or achieving.

There are three Genitive words in a row (статуса всей команды). Are they all Genitive for the same reason?

No, they are doing two different jobs. Статуса is Genitive because it is the object governed by the verb касался. However, всей команды is Genitive to show possession—it translates to "of the whole team." Stacking Genitives for different grammatical reasons is very common in professional or academic Russian.

Could I use целой команды instead of всей команды here?

Stick with всей (from весь). While both translate to "whole," весь means "all of" or "the entirety of" a group. Целый is typically used to emphasize that something is physically unbroken, intact, or impressively large (like waiting "a whole hour"). For groups of people or organizations, весь is the natural choice.

If the project is already finished, why is the imperfective verb касался used instead of a perfective form?