What are three superstitions in chapters 6-8 of The Adventures of Tom Sawyer?

In chapter 6, Huckleberry asserts that dead cats cure warts.  However, Tom insists that spunk-water (the rain-water collected in an old rotten stump) is better at curing warts.  He even proves it by telling the story of a man who did it with success.  Huckleberry argues that it has to be done a certain way, at midnight, and gives the exact steps that must be taken as well as the magic words to say.  Tom also explains how to remove warts with a bean and Huck returns by explaining how to use the dead cat.  Huck also explains how witches cast spells - by saying the Lord's prayer backwards.  He insists that one cast a spell on his Pap once.

In chapter 8, Tom is disappointed that one of his superstitions had failed.  His marble, which he had recited incantations over, hadn't produced his other lost marbles.  So instead, he speaks magic words to get a little black bug to come out, who, by not telling him anything, indicates that a witch made his spell not work.  Then  he tries another superstition by trying to get the marble to locate its lost "brother".  His third try is successful.

What are key superstitions in The Adventures of Tom Sawyer and their importance?

In The Adventures of Tom Sawyer, superstitions are important because people feel that with these beliefs they have control over certain situations. The children feel empowered by superstitions, especially if these notions seem to prove true.

One superstition that Tom holds is his cure for warts. In chapter 6, Tom runs into Huckleberry Finn. Among other things, they discuss ways to remove warts. When Huck claims that dead cats are effective, Tom asserts that he has a better method; namely, using spunk-water. According to Tom, the person goes alone to the middle of the woods, where there is "a spunk-water stump." When midnight comes, the person with the wart on his hand backs up to the stump and jams his hand inside while saying,

Barley-corn, Barley-corn, injun-meal shorts,
Spunk-water, spunk-water, swaller these warts. (Ch.6)

Then, the person walks away swiftly, going eleven paces with his eyes closed; after this, he turns around three times. After doing these things, he walks home without talking to anyone. "If you speak to anyone, the charm's busted," Tom warns. After listening to Tom, Huck says that this method is not the one that Bob Tanner has. Tom, however, gives Bob Tanner no credibility because he claims that Bob is "the wartiest boy in this town."

In chapter 9, Tom and Sid say their prayers and climb into bed. Tom waits for Huck to come by so that they can go to the graveyard and test Huck's theory about dead cats' ability to remove warts. As Tom waits anxiously, the old beams in the house seem to "crack mysteriously" and "the stairs also creak." Then a cricket begins its annoying chirping that no person could locate.

Next the ghastly ticking of a deathwatch in the wall at the bed's head made Tom shudder—it meant that somebody's days were numbered. (Ch.9)

Later Tom is undoubtedly convinced of this superstition because he sneaks out of the house when Huck Finn comes by, and they go as planned to the graveyard. There they witness the robbing of a grave for Doctor Robinson. Injun Joe is digging there with Muff Potter. When Joe wants more money for their nefarious deed, the doctor knocks Joe to the ground and wrestles with Muff, who is struck in the head with the dead man's headboard. While the two men are on the ground, Injun Joe picks up Muff's knife and kills the doctor with it. Joe then places the knife in Muff's hand. When Muff regains consciousness, Joe acts as though Muff has killed Doctor Robinson. Because Muff is a drunkard, he believes Joe; he begs Injun Joe to not tell anyone, and Joe agrees gladly. Unknown to Joe, however, is the fact that the boys have witnessed all this.

1) To remove warts, go to a graveyard at midnight and throw a dead cat at the devil when he appears.

2) Put quicksilver in bread and set the bread to float in a river to find a drowned body.

3) Worm crawling across your legs means you will get new clothes.

4) Bracelet of rattlesnake rattles will protect you from cramps.

5) Friday is an unlucky day.

6) Haunted houses exist.

7) A cross on the wall wil protect you from a ghost.

8) Howling dog = death.

These superstitions are important to Twain's themes in this story.  Consider these words from the preface:

"The odd superstitions touched upon were all prevalent among children and slaves in the West at the period of this story -- that is to say, thirty or forty years ago.   Although my book is intended mainly for the entertainment of boys and girls, I hope it will not be shunned by men and women on that account, for part of my plan has been to try to pleasantly remind adults of what they once were themselves, and of how they felt and thought and talked, and what queer enterprises they sometimes engaged in."

Twain is painting a portrait of an area and showing all the regional beliefs that control behavior in that area.  He is also demonstrating the hypocrisy and illogical nature of human behavior through the superstitions.  As readers, our attention is called to the fact that these are silly beliefs.  However, they do control the behavior of characters, showing how ridiculous humans can be.