Join Date: Aug 2009
Location: Washington, the state
2 to 3 cm of chain slack is right, about 7/8" to 1-1/4". As said above, once broken in it will rarely need readjusting until it is dying.
Sight down the chain off the rear sprocket to be sure it runs off straight is good.
That nut is probably galled on the axle threads. Order a new axle & nut. Twist the old one off or cut it off. Put a dab of antiseize paste on the new threads and torque to about 58 lbs-ft.
"Older people who are reasonable, good-tempered, and gracious will bear aging well. Those who are mean-spirited and irritable will be unhappy at every period of their lives.
"Let each of use properly whatever strengths he has and strive to use them well. If he does this, he will never find himself lacking."
Marcus Tullius Cicero