Who/what ties together the characters/movie?

If I understand your question(s) correctly, Vincent Vega, played by John Travolta, is probably the closest character to tying all of the events and characters together as most of the events involve him. If you were to take all of the events and re-arrange them so that they were in chronological order then it would be as follows...

1. Vincent and Jules drive to Brett's apartment, kill him and his associates.
2. Vincent and Jules leave Brett's apartment with Marvin, Vincent "accidentally" shoots Marvin in the head, and they travel to Jimmie's house.
3. The Wolf helps Vincent and Jules clean up the blood and guts from the car.
4. Vincent, Jules, and The Wolf arrive and Monster Joe's to demolish the tainted car, and dispose of Marvin's body.
5. Vincent and Jules head to the diner, where they encounter Pumpkin and Honey Bunny who rob the restaurant.
6. Jules and Vincent leave the diner and go to Marsellus' club where he is talking to Butch about throwing the fight.
7. Vincent and Butch have their encounter at the bar.
8. Butch keys Vincent's car.
9. Simultaneously
   • Butch throws the fight, gets in the cab with Esmerelda to take him the hotel, makes love to Fabienne, etc. etc.
   • Vincent goes to Lance's house to score some heroin, then proceeds to the Wallace house to pick up Mia, takes her out to Jack Rabbit Slims, takes her back home where she O.D.'s. Vincent takes her back to Lance's house to get the adrenaline shot, then takes her back home, and goes home himself.
10. Marsellus gathers his men to hunt down Butch.
11. Simultaneously
    • Vincent steaks out Butch's apartment.
    • Butch and Fabienne have the argument about his fathers gold watch, and Butch returns to the apartment to pick up his gold watch.
12. Butch kills Vincent when he comes out of the bathroom.
13. Butch leaves and starts to head back to the hotel, but encounters Marsellus at the intersection and runs him over.
14. Marsellus chases butch into the gun shop, where they have their fight.
15. Maynard knocks out Butch and Marsellus, and then takes them down to the basement, ties them up, and calls Zed.
16. Zed arrives, heads down to the basement and he and Maynard rape Marsellus while Butch escapes upstairs, has a change of heart looks through variuos weapons and decides on a katana, then returns down to the basement and kills Maynard, etc. etc.
17. Butch leaves, takes Zed's motorcycle chopper and returns back to the hotel to pick up Fabienne.

There are plenty of more detailed outlines available on the Internet.