Looks like regular framing lumber to me and definitely should not be left 100% exposed like that. I would paint it, caulk well and then wrap it in aluminum were it me.

Why are your door hinges on the exterior if you're in a snowy area of the country? And why wasn't that bottom sill finished before you moved in?

There are sticky weatherproofing membranes available in rolls intended to wrap such sills prior to trimming it out and painting; we had to do this for a self- installed patio door years ago and I believe we ordered the product online. Alternately, a better lumberyard will be able to advise you on what’s available in your area.

The house is very unique. It was built over 100 years ago originally. i think that back door has hinges to the outside because the house is tiny and opening inside would cause space to be lost. Also Also, there may have been a back porch there in previous years. i have no idea why the sill wasnt finished. i am trying to find out here what to do!,

It looks like more than the doors, the adjacent walls do not overhang the foundation wall/slab. So that caulk bead is all that is keeping the water from rotting your wall bottom plate. For both door and wall, you need flashing that extends over the lip of the concrete.

That wood will dissolve eventually. The area needs to be capped and sealed at the very least. Suggest you get either door/window guys or exterior finishing specialists to advise.

I also suggest you look into hinges for doors that open out. We have that here in FL because of wind but the hinges are built differently so they can't be picked.