A monster equipped with “Double Tool C&D” only negates a monster’s effect during your turn while the 2 monsters are battling. This means that it only negates effects that activate on the field, or are continuous effects while on the field. Effects that activate in the Graveyard like “Sangan” are not negated.
If, during your opponent’s turn, the opponent’s monster attacks your monster equipped with “Double Tool C&D,” and is destroyed by battle, the effect of “Double Tool C&D” that would destroy that monster does not activate.
If you have two monsters, each equipped with “Double Tool C&D,” your opponent cannot attack.
When a monster equipped with "Double Tool C&D" attacks a monster and that monster is not destroyed by battle, the effect remains and the monster's effects are negated for the remainder of the Battle Phase.
When a monster equipped with "Double Tool C&D" attacks a monster and a replay occurs, if the equipped monster attacks a different monster, then the originaly attack target's effect remains negated during the Battle Phase.
During your opponent's turn, when the monster equipped with "Double Tool C&D" is attacked and destroyed by battle, "Double Tool C&D" is also destroyed and is not on the field at the end of the Damage Step, so the opponent's monster is not destroyed.
The effect of "Double Tool C&D" will only negate effects which activate on the field, or Continuous Effects which are applied for as long as the monster remains on the field. It cannot negate effects which activate in the Graveyard, like the effect of "Sangan". If "Winged Kuriboh LV10"/"Cyber Valley"/etc is attacked, then its effect can be activated, but the effect is negated because it was activated on the field.