Hi SAL,
I assume you are doing a *BEAST analysis (using the StarBeast template in BEAUti). Trees should be linked if genes share the same history — so mitochondrial genes all have the same history and should be linked, but nuclear genes typically don’t share a history so in general should have one tree each.
The parameters for bModelTest are all estimated, and the priors on rates, the models and other parameters are fairly broad, meaning they cover most cases. If you have any extra information about rates, rate heterogeneity or proportion invariant, you can use that information to change the priors on these parameters in the priors panel. More details in the paper
http://biorxiv.org/content/early/2015/06/11/020792. Having the site models unlinked seems sensible (if there is sufficient data) since each gene will have its own rate and mechanism of evolution, but if you find that estimates for all parameters of two or more site models are close, you could link them and save estimating a few parameters, resulting in faster convergence and better fit of the marginal likelihood.
With clock models it is probably best to start with the simplest case; a shared strict clock with estimated substitution rates. If that converges, try a relaxed clock shared by all genes, and if that runs fine you can unlink the clock (but stop estimating substitution rates, since independent clock rates make it impossible to estimate both these parameters, more here:
http://beast2.org/2015/06/23/help-beast-acts-weird-or-how-to-set-up-rates/) and see how that fares.
Cheers,
Remco