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I don't know exactly what the Spanish called this forage cap but it was called a pillbox hat/cap in other militaries (notably the British army) and was worn for garrison dress. E.M Barretto's Recuerdo de Manila shows a portrait of of a Guardia Civil soldier wearing the same pillbox hat worn by the soldiers here and said uniform was described to (traje) de cuartel or garrison dress. For campaign dress, it's more likely that the jipijipa, the teresiana, or the pith helmet (occasionally a black version) would be used.

They’re soldiers so it is expected that they are lean and tanned from their field work.

Filipinos in general didn’t wear shoes en masse before the 20th century if you look at Tipos del Pais watercolors from the first and photographs from the latter half of the 19th century. Soldiers were issued shoes but did not wear them on duty out of habit/comfort/practicality. If you look at the ground they’re standing on, the first photo’s is muddy and the second’s is dry.

The second photo also has the men and officer in “In place rest/En su lugar descanso” so perhaps the shoes were worn because it was more staged/planned than the first.

Native prefer being barefoot