Another tidbit I failed to mention about Mexican sage in the northern reaches of its winter hardiness is to plant in early in teh growing season so that it can have as much time to establish itself beyond that container rootball before its first winter. This is particularly true with heavy clay soil since container peat media and mixtures thereof do not readily "mesh" with the compact, fine particles of clay in the planting hole as nicely as a loam or amended sand.

Yes. Divide away. If your plant is that big you could divide it into many plantlets.

If that is Salvia leucantha, Mexican bush sage, it does very well in clay soils. It may die back to the soil, but should come back in Spring unless it was exceptionally cold. I prefer the S. leucantha "midnight" which is an all-purple flower stem. I don't know your zone well enough to suggest companions - in CA, poppies, primrose, verbena and other sages look good with it. I have it next in front of Tagetes lemonnii (lemon marigold bush) and the purple and gold look great together.

That would be a new one for me. There are a lot of plants that can produce dermal problems, like members of the carrot (Apiaceae) and rue (Rutaceae) that produce furanocoumarins. Heracleum mantegazzianum (hogbane, giant parsnip) is a splendid example. Primula obconicais another example. Salvias may produce some compounds that may cause really rare cases of sensitivity, but I know of no examples..