I have almost the same jack but branded Lincoln and a C series. Bought a nice rebuild kit from a seller on ebay (NorthCoastHYD, no affiliation to me) in Ohio.
You're right that a nail missed the batten strip. However there shouldn't be water under the tile and it looks like it's been ponding against the high side of the batten.
Need a roofer.
Most likely the substrate was contaminated by chlorides, sulfates, or nitrates, resulting in under-film corrosion. Could try washing with a product such as chlor-rid before before and after blast.
^^This. That structure has very little lateral load resistance so seismic performance remains tied to its light weight. I wouldn't remove those braces and would not be adding weight up high.