You can possess enemies to throw themselves off ledges, at vicious animals, into meat grinders, or under falling rocks, but that's not really suicide at this point.
Characters can get crushed under falling rocks and meat choppers. When this happens there is an animation of guts flying across the screen as well as a crushing sound effect.
The screen shakes when bombs explode, rocks fall, and characters fall to their deaths, as well as when Abe occasionally uses the Shrykull Ring power later on in the game.
No, however, Abe's hands are tattooed via electrocution when he's given the Shrykull Ring power. This appears painful for him as it's happening but he's unharmed afterwards. Characters can be electrocuted to death.
Some of these deaths happen off screen after the character has fallen. The ones that happen on screen have the animation and sound effect of splatting on the ground.
Certain areas have rapidly flashing lights that are accompanied by an alarm siren going off. Bombs, gun shots and electrocutions have flashing effects, as well as when Abe occasionally uses the Shrykull Ring power later on in the game.