Why do the faces deform and intersect. I want them to be a flat square face not a caved in triangle faces.
That fold is a non-planar face. BSP stores a polygon, then the build triangulates it. If the four corners of that “square” are not on one plane, one triangle tips inward and you get a caved-in triangle instead of a flat quad. Intersecting faces are the same thing when two brushes share a plane.
What to change:
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Put the corners back on one plane. Turn on grid snap and vertex snap, then drag the high corner back down. Look at the face from the edge: if the four points do not line up, it will fold no matter how you rebuild it.
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Do not scale or rotate the brush off the grid. BSP is snapped integer geometry. A non-uniform scale or an off-axis rotate makes the polygon slightly non-planar and the two triangles cross. Snap it, then Build → Build Geometry. Avoid non-uniform scale on the brush.
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Coplanar brushes intersect. An additive brush sitting flush with a subtract (or two additives on the same plane) produces the triangle fighting in the middle of the wall. Separate them by at least one unit, or push the subtract clearly through instead of leaving it flush.
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If this is not a simple room, stop using BSP. It is legacy in UE5 and it will keep folding on anything that is not an axis-aligned box. Right-click the brush → Convert to Static Mesh, or rebuild the piece with the Modeling tools, where you can force a face planar.
Rebuild geometry after the snap. If it is still a triangle, one vertex is still off the plane.