Question: How long is typical for a reasonable amount of time to re-commence play after a foul?
About the article "Water polo", section "Setting the ball".

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The key to the offense is to accurately pass (or "set") the ball into the center forward or hole set, positioned directly in front of the goal ("the hole").
Any field player may throw the hole set a "wet pass."
A wet pass is one that hits the water just outside of the hole set's reach.
A dry pass may also be used.
This is where the hole set receives the ball directly in his hand and then attempts a shot at the cage.
This pass is much more difficult because if the pass is not properly caught, the officials will be likely to call an offensive foul resulting in a change of ball possession.
The hole set attempts to take possession of the ball a wet pass, to shoot at the goal, or to draw a foul from his defender.
A minor foul is called if his defender (called the "hole D") attempts to impede movement before the hole set has possession.
The referee indicates the foul with one short whistle blow and points one hand to the spot of the foul and the other hand in the direction of the attack of the team to whom the free throw has been awarded.
The hole set then has a "reasonable amount of time" (typically about three seconds) to re-commence play by making a free pass to one of the other players.
The defensive team cannot hinder the hole set until the free throw has been taken, but the hole set cannot shoot a goal once the foul has been awarded until the ball has been played by at least one other player.
If the hole set attempts a goal without the free throw, the goal is not counted and the defense takes possession of the ball, unless the shot is made outside the 5-meter line.
As soon as the hole set has a free pass, the other attacking players attempt to swim (or "drive") away from their defenders towards the goal.
The players at the flat position will attempt to set a screen (also known as a pick) for the driver.
If a driver gets free from a defender, the player calls for the pass from the hole set and attempts a shot at the goal.
Like all fluorescent lamps, the low pressure lamps will burn for a long period of time.
They will, however, lose their ability to produce a reasonable amount of UV after a short while.
Typical lifespans for low pressure lamps are from 300 to 1,600 hours of actual use although they may light and produce very little UV for as much as 5000 hours.
High pressure lamps range from 300 to 1,000 hours, and should be replaced when they have reached their maximum life to prevent any possible damage to the ballast, although this is very rare.
Lamp manufacturers generally rate the "life" of the lamp to be the period of time that the lamp will continue to emit at least 70% to 80% of the initial UV. 
In the National Basketball Association, bonus rules in a quarter apply starting with the fifth team foul.
The NBA rules on the team foul penalty are similar to the FIBA version, with three major differences.
Only defensive and loose-ball fouls count towards a team's limit for the team foul penalty.
Offensive fouls do not count towards the team foul penalty.
The team foul penalty applies in a period after a team commits one foul in the final two minutes if the team had not reached the penalty phase in the first ten minutes of that period.
In other words, within any period free throws are awarded starting from the fifth foul OR from the second foul in the last two minutes of the period, whichever comes earlier.
If a game enters overtime, the foul counts are reset to 0, and are similarly reset before each subsequent overtime period.
The penalty phase starts with the 3rd foul in each overtime period rather than five for regulation periods, since overtime periods are so much shorter than regular game periods (five minutes vs. twelve in regulation play).
As is regulation play, two free throws are awarded for non-shooting defensive fouls during the bonus period, and one foul in the final two minutes automatically puts the team in the team foul penalty. 
In sport, a professional foul is a deliberate act of foul play, usually to prevent an opponent's scoring. 
Number of players.
Seven players from each team (six field players and a goalkeeper) are allowed in the playing area of the pool during game play.
Each team may also have six additional substitute players, and up to one of these players may take the position of the reserve goalkeeper.
If a player commits a major foul, then that team will only have 6 players until the player is allowed to re-enter.
If a player commits a brutality foul, then that team must play without that player, or any player taking his or her place, for 4 minutes.
If at any time during play a team has more players in the pool than they are allowed, a penalty is given to the opposing team.