Sorry if this was covered recently but I can't quite make a ruling on this from the rulebook, couldn't find the answer with the search function, and can't find it in the PG. Thanks.

Does the corner of a square of wall terrain qualify as along the edge?

Can a figure in a diagonally adjacent square to a square of wall terrain, destroy the wall with close combat?

If a figure has a perfect diagonal line of fire through the corner of a square of wall terrain, to the center of the square on the other side of the wall, and is within range. Can the figure destroy the terrain via ranged attack?

Also, does the figure have to have 3 printed damage? Or can the damage value be modified to 3.

You cannot use close combat to destroy a wall at a diagonal. The square the character occupies and the the wall must share an edge.

As far as ranged, the LOF has to pass between two squares that share an edge, so you also would not be able to destroy a wall at a diagonal.

As long as you can legally do 3 damage you can destroy blocking terrain.

Any character with Super Strength can destroy walls/blocking/objects with a close combat attack as well.

SUPER STRENGTH - When this character moves due to its own action, it may
pick up an object and hold it. The object must be either in a square the char acter
occupies or in an adjacent square. If this power is lost or countered while this
character is holding an object, immediately put the object in the square this char acter
occupies. When this character makes a close combat attack targeting blocking terrain,
a wall, or an object, modify its damage value by +2 for the attack.

Except Ultron-13 on his 3rd click (he has SS and 0 damage).

Not at all true. While SS gives a +2 you still need at least 1+ DV which may not be the case if Perplex is involved.

There's always a %$^$&# exception...

Generally speaking, ALMOST every figure with Super Strength can destroy a wall.