壁 and 柱: walls and pillars
Name parts of a building and distinguish figurative uses.
A wall's location
壁 (かべ) means wall. 「壁に地図を貼りました」 means putting a map on the wall.
「壁の向こうから声が聞こえます」 says voices are audible from beyond the wall, not that the wall itself is speaking.
A pillar's location
柱 (はしら) means pillar. 「柱のそばで待っています」 means waiting beside a pillar.
「柱で画面が見えません」 says a pillar prevents the screen from being seen. で here marks the cause of the obstruction.
Figurative references
「言葉の壁を感じました」 describes experiencing a language barrier, not a physical brick wall.
「教育を計画の柱にします」 makes education a central element of the plan. 柱 figuratively names a supporting core element.
Is 「計画の柱」 a pillar to be built in a building?
Show the answer and why
In this context it is a metaphor for a central element of the plan, not a physical building part.