'98 Sub vibration, slight "clinking"

I have a '98 Suburban with 233,000 miles on the 6.5 turbo diesel and just this morning I noticed when I come to an idle it seems to run a little rough, almost like it's missing on one cylinder. It continues to do so until it gets up to about 10 mph then goes away. Later this morning after driving it and then stopping, I hear a slight "clinking" sound at idle. Not a terribly loud "clank", but rather a milder sound. I'm wondering if this would be the harmonic balancer, and if so, would it cause both symptoms? To my knowledge it has never been replaced, but I am not the original owner and don't know for sure.

Thanks in advance.

A buddy of mine and I looked at the harmonic balancer, and when the engine is shut off you can see part of the unit keeps spinning for a couple of seconds after the main pulley has stopped rotating. There appears to be a shiny metal section immediately behind the pulley, then a larger, slightly rusty circular part (partially hidden by the front of the engine) immediately behind the shiny piece. It is that rear piece that keeps spinning. Is this normal?

No.

No.
I'll uh second that one, NO!

Well, then I guess I've got a job to get done. Being new to the 6.5 TD engine, is there anything else I should check/replace while taking care of this matter? How risky is it to drive it the way it is if I must do so?
Thanks for the input, guys.