If you go through Saltillo there are no tolls until south of Aguascalientes into Guadalajara. Neveretheless, you will find the Matahuala to San Luis Potos leg a rather boring and much trafficked route. However, if you insist on the Matahuala route, be sure and spend an extra day visiting Real de Catorce out of Matahuala. San Luis Potos can be interesting, but only if you know what you are looking for. Not like Zacatecas where every turn you find something new.
Roads are good both ways.
Ten years ago you had to buy a special permit for the dog. It ran about 20 us dollars. My friends tell me that is no longer true, that all you need is proof of recent rabies vacinacion and no special papers. You might check. The trip south of Monterrey, no matter which route you take is all semi desert.