How dangerous are these soil organic carbon digestion methods?
$\pu{0.1 M}~\ce{NaOH}$ is potentially corrosive when in contact with metals or human skin (see here), so I advise precautions such as wearing protective standard gloves and keep metals away from feasible damage.

$\ce{HCl}$ and $\ce{H2SO4}$, especially when they're hot and are in higher concentrations, are very corrosive acids that are dangerous in contact with many materials. They can also release noxious gases in the reactions, but their weakness is glass. Due to reasons irrelevant, these acids can't corrode glass. I recommend extreme precaution. You can work under a "glassy" protection and as Yomen mentions, under a fume hood. Gloves are very important here. Here's what Caltech thinks about precautions using $\ce{HCl}$ and here's what Berekley does about sulfuric acid.

$\ce{KMNO4}$ is a very strong oxidizer. It may cause fire in contact with different materials (we had a volcano experiment in elementary school where we mixed it with glycerine and the result was very exothermic), and it has biohazards such as kidney damage. Here it's explained more comprehensively.