My identification strength (for some variables) result is near 0 like the following, and the model check plot also seems wrong. however, it doesn’t produce error info. May I know if this is a problem and how to fix this? Thanks a lot!

Sorry that I might be mixing some concepts. I am still a little confused that since the absolute value of the bar suggests the strength of the identification, I am thinking since the value is near zero, that might suggest a weak identification?

Also as I change the prior mean and standard deviation, the posterior mean changes accordingly around the prior mean I gave, this gives me a sense that the prior is kind of fixing the posterior, which seems like a sign of bad identification? also, e.g. rho_z, which has a very flat posterior likelihood (a sign of bad/weak identification？), but its prior and posterior graph shows the posterior is far away from the prior (a sign of data did some work? at least posterior not equal to prior), I don’t understand why is this, may I know a little more about this.

Looking at your graphs, some parameters are more strongly identified than others. But even for strongly identified parameters, the effect of a prior will only vanish asymptotically. Thus, it’s not surprising for the prior to matter.
It is very uncommon for some parameters to be rather weakly identified. But that does not mean there is a big problem. The data will still matter (unless the parameter is not identified at all) and consistent with that logic, prior and posterior are different in your plots. That suggests that everything works as expected.