A corpse-spawned player acts and behaves almost like an ordinary dead body: they cannot move, shoot, or perform any other action. However, they can look around, with the camera anchored inside of their head. Other players can hear the affected player on proximity voice (if said player has a microphone), and the player's gamertag is displayed above their body when another player aims at them. The player will also see "Hold RB to..." messages on-screen, though holding RB will have no effect.
It is possible for players in this state to actually pick up weapons. If a glitched player is meleed or otherwise moved onto a weapon, they may actually pick up the weapon; on the glitched player's screen, they will appear to be holding the weapon normally, and to others, the weapon will appear to be glued to the corpse's hand.
Furthermore, such corpse-players are regarded by the game as living bodies -- their deaths don't count as deaths. If, for example, a player corpse-spawns in an Infection game, then they will become the Last Man Standing, and the game will not end until their corpse dies through some other means (specifically, by falling to its death).
Other odd quirks include the inability to launch glitched players off of Man Cannons; meleeing a corpse-spawned player onto a Man Cannon will cause them to launch out of the cannon before quickly warping back to the cannon. The same happens for any force that significantly displaces the glitched player's body, including grenade explosions. Furthermore, it may be possible to separate a corpse-spawned player's camera from their body.
In Theater, an additional oddity occurs; if one watches a Film of a corpse respawn, and detaches the camera from the glitched player (so that it is not in first-person) after they respawn as a dead body, then it will be impossible to get back into first-person view for any player in the match.
Finally, if one looks closely at a player-corpse while that player looks around, one will notice that the corpse's head and held weapon (if any) both rotate slightly as the player looks around.
When a player spawns, a player model is placed on the map for them, and their camera and controls are bound to that model. When they die, a new model is created for them, and their camera and controls are bound to the new model.
This glitch happens when the game lags. It is possible that the lag prevents the creation of a new player model, causing the affected player's camera and controls to be rebound to their corpse -- it's still a player model, albeit an unusable one.
 The View
The reason that corpse-spawned players can see their midsection but not their upper bodies is that no player -- alive, dead, or both -- can see their own upper body. When in first-person view, a player's upper body is made invisible, so that things like armor features don't impede a player's vision. The reason that a player can (sometimes) see their own arms is because they're actually looking at "fake" arms, which are only visible in first-person view and which react to the player's movements, but don't adjust to account for, say, the player's death.
 Picking up a Weapon
Corpse-spawned players respawn without any held weapons. If, however, they come in contact with any weapon, through any means, then they will immediately and automatically pick that weapon up. The same thing happens with unarmed players that are still alive -- corpse-spawned players are basically living players whose bodies can't move and won't respond to button presses.