In cricket, umpires can declare a batsman out only if the fielding team appeals for it but in obvious cases like bowled and caught the fielding team does not appeal because the batsman itself walks away but if the ball hits pads or catch where the ratio of getting out is 50:50, then you will only get the wicket if you appeal for it. If the fielding team doesn't appeal, then even if the batsman is out the umpire can not declare it out.
"Time is money" also applies to cricket. You might have seen that captains get penalized for slow over-rate because every side has to bowl their over quota in a specific interval of time. Only the fielding side can be penalized in a slow over-rate. According to law number 40 of cricket, after the dismissal of the batsman, the incoming batsman must be ready to face the ball or be in the crease with his partner within 3 minutes of the outgoing batsman. If the batsman takes more than 3 minutes and the fielding team appeals for it, the incoming batsman can be declared out.
To make sure that every side gets equal rights, the rule of penalty exists in cricket. According to this rule, if the fielding side intentionally damages the ball or pitch or if the ball touches the equipment of the fielding side which the player has not worn (for eg - gloves, helmet, etc), then the batting side gets five additional runs. If both the batsman cross each other before the ball hits the equipment, this extra run is also counted and the ball is not counted in this rule.
One of the rules of caught out in cricket states that batsman cannot be declared out if the ball hits the batsman on the glove and his caught but the hand or the glove is not in contact with the bat. During the final test match at the Lords between England and Srilanka in 2014 June, Rangana Herath was caught with the ball hitting his glove that was not in contact with the bat. Umpire has not ruled Herath out but he walked away because he did not know the rule.
You cannot have more than two fielders behind the square on the leg side in all forms of the game. This is done keeping in mind the spirit of the game because the bowler can have fielders on both sides behind the batsman and can keep on delivering bouncers which could cause physical harm to the batsman. That's why two bouncers over shoulders height in an over is declared as a no-ball keeping the spirit of the game.
Batsman trains vigorously for years to play fastballs that come to them at a speed of 140 to 160 kmph but when it comes to less than 50kmph, their mind just doesn't work and they commit the ultimate mistake in cricket trying to handle the ball with their hands. Although the player can use the bat and his legs to stop the ball but using hands is against the rule. Also, the batsman cannot try to stop the ball intentionally while running between the wickets. This is considered as obstructing the field.
We all know that cricket captains have a lot of powers. One of the power is that the captain can recall the dismissed batsman if he thinks that the batsman is undeserved or he isn't satisfied, then he can withdraw his appeal and can call the batsman to the crease again. Undeserved dismissals usually happen when the batsman gets run out with an injury or collide with a player and gets out. Something like this happened in 2011 (Ind vs Eng) match where Dhoni called Ian Bell after he was declared run out.