What is the price and armor check penalty of a Mithral Breastplate?
Well, you have the breastplate:
Then the effects of mithral:
So when we combine them:
Unfortunately, they don’t tend to put special materials in neat tables like the one I just made for Mithral, so you have to read carefully to determine its effects, but generally speaking the process is the same as what I’ve done here: you figure out what the material modifies, and just apply each one.
About Armor Check Penalty, the rules are less clear: they never explicitly say that the Armor Check Penalty reduction of the mithral includes the Armor Check Penalty reduction of being masterwork armor. Consulting with various example mithral armors,1 however, it appears that it is included (i.e. the total reduction in Armor Check Penalty is −3, not −3 for mithral and −1 for masterwork). The rules for adamantine armor are a little more clear on this point, and the formatting of each material should be consistent.
Note that, by strict RAW, this isn’t exactly definitive; the primary source on this is the rules text for mithral itself, which is ambiguous. You could make an argument that the masterwork effect is not included, and then that the example armors are mistaken, and that nothing says that adamantine and mithral have to handle this the same way. Since the rules for mithral are merely ambiguous, rather explicitly in your favor, I’d be shocked if any DM bought it, but the argument could be made and I might buy it for a TO exercise or something. But then I’d also consider houseruling that you get both (i.e. ACP 0) just because I might be convinced things are better that way.
1 Thanks to mxyzplk to pointing those example armors out.