I have 02 Z71 ,and had same problem(s).
Noticed right tire was cupped. Replaced tires, helped some what.( I am anal about tires anyway ). Took to dealer and complained about that, leaking right front shock, and clicking noise in steering column.
Dealer called next day and said 3 of the new tires were bad ? But they replaced front shocks and lower steering shaft under warranty and told me to go to the tire dealer and get 3 new ones.
Picked it up that night and got on interstate and guess what ? problem solved !
I did take it back to the tire shop and had them " road force match balance" tires again ( because i'm anal ),and just got back from a 750 mile trip and no problems.
Just fyi,
snidelywhplsh