I'm thinking they're not original to the house. Back in the day registers were in the floors. And the style is wrong for the age of the house.

Yes they are inappropriate, and probably not original. Nor is the baseboard. So. I imagine the originals were replaced when the house was "updated" at some point with this modern baseboard and "new and improved" registers.

Wall registers were introduced with gravity-fed central heating, so wall registers re appropriate for the period of the house, just not these wall registers.

The originals probably looked something like this restored register:

Fortunately,, reproduction registers are easy to find, as is period-appropriate baseboard (see picture). Just do a Google search on "1900 heat resisters."

Our late 1920s (Spanish Revival) house has the registers StarCraft posted a pic of above. Here is what they look like:

(It's painted that cream color to match the door/window trim and picture rail.) Ours has the decorative top of the baseboards continuing around the register. Your baseboards are simpler, but you could consider having that tapered top continue around the register.

Not original or significant. And whoever put them in didn’t bother to use a screw with an appropriate head.