To your first question: you could enter any expression, even use a
dependent variable. That's why comsol works with time steps.
To your problem with solving/meshing: it's nearly impossible to say
what your error could have caused, not knowing your geometry/meshing/
solver_settings/hardware etc. Different error messages seem to me
like a fundamental problem in your model. How many degrees of freedom
would you have after meshing your model?
btw, and more importantly: why wouldn't a coarse mesh be exact
enough? Did you do a quality mesh and check for consistency? Couldn't
your problem be reduced to a 2D-problem anyway, which is very much
probably if you're able to apply a mapped mesh?