21. Biggest difference in strongness between 2 players in a draw game.

World Championship 1968. 
Young Dutch player Harm Wiersma, who was one of the favourites for the world title, played against L. Reimann from Austria, who was one of the weakest players in international tournaments ever. Only Feldl, also form Austria, was weaker. Wiersma couldn't win against Reimann.

White: H. Wiersma - Black: L. Reimann

Was Reimann really so weak? Yes, he was. On the Challenge Mondial 1962 he played, with the white pieces, against the draughts clown of Monaco Agliardi 33-28 (18-22) 39-33. Of course black won two pieces, but coudn't win the game (draw)!
In the invitation tournament of Yalta 1963 Reimann played his 17th game on international level. Against M. Verleene from Belgium he played 32-28 (18-23) 37-32. Verleen won two pieces and the game. 
Nowadays it will be impossible: Reimann&Feldl in international (closed) tournaments!

22. Biggest difference in strongness between 2 players, but... the weakest player won.

Maybe I. Koeperman - P. Bebel (Guadeloupe 2000).
Iser Koeperman, seven times world champion, against Patrick Bebel, a player from French Caraibic island Guadeloupe, without a rating.

In this game, Bebel played extremely good and Koeperman, although he didn't make a big mistake, lossed the game.
In the other games of the tournament Bebel produced only draw games and losses.

White: I. Koeperman - Black: P. Bebel

Bebel, after the tournament, to his wife: Darling, I didn't make anything in the tournament. Draws and losses. I only won a game against former world champion Koeperman!

Perhaps a better and a more historical candidate is the game R. Dagenais - R. Forclaz, World Championship 1952.
It was the last round. Canadian Dagenais needed only two points to become world champion and his opponent in the last round was Forclaz from Swiss, the weakest player in that tournament with only 2 draws and the rest losses.
Dagenais tried and tried and tried, but he couldn't take any advantage in the game. When he took to many risks, he lost the game...

23. Biggest difference in temps in a game with the same amount of pieces for black and white.

A. Kooimans - J. de Hei (1982, The Netherlands) on the 48th move. White has offered his king with 12-40.

White: A. Kooimans - Black: J. de Hei

Black has 29 more temps (but losses the game).

24. Biggest difference in temps in a game with the same amount of pieces for black and white. And... there was no king at all in the whole game.

A game between A. Janse and J. Poppe (SNS tournament, 2001, Netherlands): 24 temps.

White: A. Janse - Black: J. Poppe 

A better game, with a difference of 23 tempi, was P. Moerenhout - J. Geuke, Brunssum 1990. 

25. Most kings together in a game

L. Camara - M. Jaggoe (World Championship Youth 1985). 
After 84 moves there were 7 kings together. White 4, Black 3. It's the only game in world history with 4 against 3 kings.

White: L. Camara - Black: M. Jaggoe 

A game with 5 against 2 kings is more common. It's a difficult endgame; the player with the 5 kings has a winning position, but some players don't know how. 
One example: Herman Meijer - M. Visser (Netherlands, 1984). After 128 moves and 9 hours Meijer accepted that he didn't know how to win and proposed a draw.

26. Biggest shot

E. Sinke (The Netherlands) beated not so long ago 9 pieces in one move. It's a world record!

White: E. Sinke - Black J. van den Ouden 

1. 33-29, 18-23; 2. 29x18, 12x23; 3. 31-26, 13-18; 4. 36-31, 9-13; 5. 41-36, 4-9; 6. 47-41, 20-24; 7. 34-30, 8-12; 8. 39-33, 24-29; 9. 33x24, 23-28; 10. 32x23, 18x20; 11. 44-39, 20-24; 12. 49-44, 12-18; 13. 37-32, 7-12; 14. 41-37, 2-8; 15. 46-41, 18-23; 16. 39-34, 13-18; 17. 30-25, 15-20; 18. 32-27, 17-22; 19. 43-39, 1-7; 20. 48-43, 11-17;

Black resigned (of course!).

According to Turbo Dambase (a database with more than 250.000 draughts games) there are in world draughts history only 6 games in which a piece or a king beats 8 pieces.
Three examples.

White: G. Geurts - Black: P. van Harten (Netherlands 1975)

White: I. Greveraars - Black: J. de Bijl (DAVO Vos 1985)

White: H. Ladage - Black: R. van Zelst (Championship of Gelderland, Netherlands, 1990). Spectacular but... draw.

27. Biggest shot in an artificial game

11 pieces. (Follow the link.)

28. How many pieces can a piece (theoretically) beat?

16 pieces  

29. How many pieces can a king (theoretically) beat?

This position is wonderful. It's difficult to see how it's possible to beat 18 pieces and the endfield is a strange one. See the animation.

But... it's not a world record. 19 pieces is possible. See the animation. 

Siep Korteling (Netherlands) made a composition on this theme. White plays and consequently looses(!) in only 4 moves.

30. The most moves before playing a piece on the first row. (for white: 46, 47, 48, 49, 50, for black: 1, 2, 3, 4, 5)

1950, P. Roozenburg - M. Raichenbach, a game between two world champions.
Not earlier than on the 34th move Roozenburg played with a piece on the first row. He won the game.

White: P. Roozenburg - Black: M. Raichenbach 

But it's not a world record. (Perhaps a world record in a game between two grandmasters.)

Patrick Carli played against Erno Prosman (youth championship of The Netherlands 1991) not earlier than on the 49th move (!!) with a piece on the first row. It was not sufficient for a point.
White: P. Carli - Black: E. Prosman