First, a disclaimer. I'm a SimBiology developer, not a modeler. So I'm most knowledgable about what is technically possible within SimBiology and what functionality SimBiology users have asked for.
Your first question about the size of tissues sounds like a very general issue with using ordinary differential equations (ODEs) to model the "real" world. The state variables in ODEs are continuous, so there's no concept of a single cell or single molecule. When you are dealing with a small number of items, the assumptions for mass action kinetics also break down. An alternative modeling approach for such cases is to use a stochastic solver (which models the discreteness of your state variables), but I've only seen this used to model molecules rather than tissues.
Another alternative could be to add an event to your SimBiology model that enforces a lower limit to the tissue mass/volume. For example, you could write an event with a trigger "tissueMass <= 1e-9" that then sets "tissueMass = 0" to enforce that you never have a tissue value between 0 and 1e-9. You could add additional event functions that make additional changes to the model to ensure you don't have unrealistic tissue regrowth.
As for your second question about tolerances, this sounds like the expected behavior. You need to make sure that your tolerances are set tight enough for reliable results. The specific tolerances will depend on the details of your model. You might also try toggling AbsoluteToleranceScaling to see if that makes it easier for you to set appropriate tolerances. You can read more about SimBiology's tolerances here. You might also want to recent this recent blog post about ODE tolerances.
