Can a referee caution or send off a substitute or substituted player?
From page 39 of the 2015/16 FIFA Laws of the Game (emphasis mine):
The yellow card is used to communicate that a player, substitute or substituted player has been cautioned.
The red card is used to communicate that a player, substitute or substituted player has been sent off.
Only a player, substitute or substituted player may be shown the red or yellow card.
While a substitute or substituted player can technically be sent-off for any of the seven sending-off offences a player is subject to, there are only three offences for which they may be cautioned.
p. 40 of the 2015/16 FIFA Laws of the Game:
A substitute or substituted player is cautioned if he commits any of the following three offences:
- unsporting behaviour
- dissent by word or action
- delaying the restart of play
The team will continue to play with the same number of players they had on the field at the time the substitute or substituted player was sent off.
If a substitute is sent-off before the match begins, they cannot be replaced with a reserve player who was not named in the line-up.
p. 21 of the 2015/16 FIFA Laws of the Game:
A named substitute who has been sent off, either before the kick-off or after play has started, may not be replaced.
Yes. Although the team won't lose a man, the team won't be able to use that substitute, and the player will be subject to the same disciplinary sanctions as if they'd been sent off while on the pitch.
Additionally, players can be sent off after the game has finished. They can also be sent off before the game starts, though if this happens the team can replace them and won't be a man short.