harry potter - Did Dumbledore and McGonagall cheat so the Gryffindors would win the House and Quidditch Cups?

When Harry is a first year, Professor McGonagall recommends Harry as seeker and gifts him a Nimbus 2000, breaking the house rule according to which first years are not allowed to have brooms. The idea is probably that flying (and especially Quidditch) is too dangerous, and first years shouldn't dodge Bludgers or fly unsupervised. It's allowed to fly under the supervision of Madame Hooch, on school brooms. Harry was good, but my impression was that he wasn't as good as Quidditch prodigy Viktor Krum, to justify making him the youngest seeker in 100 years.

When Harry enters Hogwarts, Slytherin house is on a winning streak for both the House and the Quidditch Cup. The Seeker is extremely important to the outcome of the game, so could it be that Minerva was desperate enough to change tactics and use a young, lightweight seeker, giving an unfair advantage to the Gryffindor team?

Later, in Harry's third year Professor McGonagall says to Harry:

"...Potter- do try and win, won't you? Or we'll be out of the running for the eighth year in a row, as Professor Snape was kind enough to remind me only last night…" _{~Harry Potter and the Prisoner of Azkaban - Chapter 12: The Patronus}

In sixth year Harry uses a spell of unknown origin that almost kills another student, refusing to tell the source that spell come from and if there's more such things he learned. Yet McGanagall has no intention to suspend Harry from the team.

Same with the House Cup. In first year Dumbledore awards exactly enough points so Gryffindor would win. How that's fair? It's not as if other houses were given the chance to fight Voldemort or had the cloak of invisibility.

There is a conversation in Philosopher's Stone when the trio discusses Dumbledore:

"D'you think he meant you to do it?" said Ron. "Sending you your father's cloak and everything?" "Well, " Hermione exploded, "if he did -- I mean to say that's terrible -- you could have been killed." "No, it isn't," said Harry thoughtfully. "He's a funny man, Dumbledore. I think he sort of wanted to give me a chance. I think he knows more or less everything that goes on here, you know. I reckon he had a pretty good idea we were going to try, and instead of stopping us, he just taught us enough to help. I don't think it was an accident he let me find out how the mirror worked. It's almost like he thought I had the right to face Voldemort if I could...." "Yeah, Dumbledore's off his rocker, all right," said Ron proudly. _{~Harry Potter and the Philosopher's Stone - Chapter 17: The Man with Two Faces}

So if Dumbledore was leading Harry and did everything to ensure he'd fight Voldemort and that he would be ready, how it is fair to award points for it?

Between Snape openly favouring the Slytherins and Dumbledore and McGonagall bending the rules and cheating do other houses even stand a chance to win?

Answer

They at least show favoritism

They did indeed show favoritism, but not all the examples you mention are cheating.

As you mentioned, Dumbledore awarded Gryffindor just enough points to push them ahead of Slytherin:

The din was deafening. Those who could add up while yelling themselves hoarse knew that Gryffindor now had four hundred and seventy-two points—exactly the same as Slytherin. They had tied for the house cup -- if only Dumbledore had given Harry just one more point .

Dumbledore raised his hand. The room gradually fell silent. "There are all kinds of courage," said Dumbledore, smiling.

"It takes a great deal of bravery to stand up to our enemies, but just as much to stand up to our friends. I therefore award ten points to Mr. Neville Longbottom."

—Harry Potter and the Sorcerer's Stone

Ten points is really a rather small reward. While one could make a good argument for awarding lots of points based on saving the world, it seems clear that the precise number of points was calculated to put Gryffindor in first place.

McGonagall also is highly biased against Slytherin, and particularly does not want to see Snape win any accolades, as evidenced in the first quote in the question.

Her attitude when awarding points at the end of Order of the Phoenix makes this quite plain.

“So that’s fifty each for Potter, the two Weasleys, Longbottom, and Miss Granger,” said Professor McGonagall, and a shower of rubies fell down into the bottom bulb of Gryffindor’s hourglass as she spoke. “Oh — and fifty for Miss Lovegood, I suppose,” she added, and a number of sapphires fell into Ravenclaw’s glass.

—Harry Potter and the Order of the Phoenix

Notice how Luna, a Ravenclaw, is merely an afterthought.

It is worth noting that in all cases in which points were awarded, McGonagall and Dumbledore had very good reason to award points. It is also true, however, that they specifically seized upon these ambiguous instances to put Gryffindor ahead of Slytherin.

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That said, there is at least one thing mentioned in the question that was not favoritism or cheating.

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  Not suspending Harry from Quidditch after his use of Sectumsempra.

  
  

  This was self-defense, to start with. Malfoy had been about to use the Cruciatus Curse on Harry:

  
  

  
  

  There was a loud bang and the bin behind Harry exploded; Harry attempted a Leg-Locker Curse that backfired off the wall behind Malfoy's ear and smashed the cistern beneath Moaning Myrtle, who screamed loudly; water poured everywhere and Harry slipped as Malfoy, his face contorted, cried, "Cruci —"

  
  

  "SECTUMSEMPRA!" bellowed Harry from the floor, waving his wand wildly.

  
  

  —Harry Potter and the Half-Blood Prince

  
  

  
  

  Second, Harry had no idea what the spell did, beside that it was offensive, and so was guilty of recklessness in a possibly lethal situation at worst.

  
  

  And while McGonagall did not suspend Harry in that case, Snape did.