Yes, the defense can return a missed field goal for a touchdown. However, the touchdown would be credited to the special teams and not to the defense since a field goal is considered a special teams play. The TD would be considered under the heading 'return of a missed field goal' and not a blocked kick nor punt return.
I', pretty sure it's at the spot of the kick
In college football, the rule for a missed field goal to the kicker's left is called wide left and conversely wide right if it misses to the kicker's right. It is described as short if it is aimed correctly but does not have the distance to go over the cross bar.
the team on the field is playing defense
Yes. A missed field goal that hits the ground results in no points and the opposing team taking possession at the spot of the kick (not the original line of scrimmage). If the opposing team catches the ball and returns it, the recovering team would instead get the ball at the point where the return ends. It is possible to return the missed FG for a touchdown.
Scott Norwood missed the field goal in the 1991 SuperBowl
In the NFL, the ball will be placed at the spot of the hold after a missed field goal. If the kick took place from inside the 20, the ball is moved out to the 20. In college football, the opposing team gets the ball from the original line of scrimmage.
the executioner 1800 is an amazingly good field hockey stick for defense