Long story short, this is pretty much spot on :P
The story of Saint Nicholas is indeed from Turkey. There are 2 stories I know (along with most Dutch who know Sinterklaas is a big, but fun, hoax).
First there is the story of the three murderd students. These three were murdered by the innkeeper. In order to hide this crime, the innkeeper decided to keep the remains in a barrel with brine. When Saint Nicholas visited the same inn, he dreamed about the crime. He then decided to call the innkeeper and started to pray to God and the students were resurrected (and the innkeeper most likeley put away, I can't remember).
The second story is about a poor man with three daughters. The man could not afford a dowry for any of his daughters. Without this dowry, the women were likely to never find a husband and be sold as slaves. However, on three seperate ocasions there appeared a pouch with gold for the women. It is said that these pouches with gold landed in the shoes which were drying in front of the fireplace.
The first story speaks of one of the miracles of Saint Nicolas, the second pretty much explains the tradition of placing shoes in front of the fireplace.
About the black men. Originally there was only 1 and there are multiple stories. One is of a slave named 'Piter' who was freed by Saint Nicolas. He was so gratefull that he decided to join the Saint. The other I know is that Saint Nicholas defeated a devil, which he then enslaved to do good in the world (or punish kids with a switch or abduct them).
Sinterklaas has a long history, but long story short is that Black Pete evolved from a diabolical creature punishing bad kids with a switch to an army of jolly helpers. Some of the songs still speak of the old Pete, saying things like:
Zijn knecht staat te lachen en roept ons reeds toe: 'Wie zoet is krijgt lekkers, wie stout is de roe'
This roughly translates to
His servant is laughing and calls to us: 'Sweets for the sweets and the switch for the naughty'
How we got the silly idea that he lives in a castle in Spain is still a mystery to me. That, and how the kids still believe it, even with the internet and all the magic needed to make it work.
And yeah, my clog was stuffed with candy. A chocolate letter 'P' and kruidnoten :) And that while the fireplace hasn't arrived yet...
To get you in the mood, 20 minutes of sinterklaas songs
EDIT: spelling and also check Krampus for another evil creature like the old Black Pete.