Hercus chuck problem I think

Am I having problems with my self centering chuck on my Hercus lathe.

I'm very much a novice when it comes to metal machining.

I've suspect for a bit that my three jaw self centering chucks are a bit off centre so today I pulled my dial gauge and had look and play.

First I put it on the spindle turned the lathe by hand and this is has far as it is out

Then I did the same with the chuck the piece in the chuck was turned between centres .

So I am pretty confer dent it is square and true

So questions are have I set up to check the main spindle correctly ?

Have I set up to check the chuck correctly ?

Is this amount of run out I think that's the correct term, ok or not on the chucks ?

Both my three way chucks are showing about the same amount of run out

If the chucks are the problem ?

I also made sure the jaws were clean before clamping down on the bar for testing.

What should or can I do about it ?????

And lastly am I making sense lol is this normal or not ?

And one last question my dial gauge good ok , bad I really have no idea about quality of this sort of stuff ?

Tho I spend a lot time in here reading all the threads pretending I understand lol.