Can anyone identify the maker of the pedal in the last photo?
Yes, those are Wippermans, form Hagen, Germany - the company is still in existance today - although they dont make pedals anymore, but still chains , for bicycles and industrial appliactions.
Wippermann pedals were widely used in Europe- this design came up around 1900 and was used into the very early 30s.
Schladitz was condisered as a high-end brand ("Markenfahrrad") but produced relatively small numbers - they made many components themselves, but had no pedals of their own, so I'm certain these pedals were originally equipped with your bike.
Any by the way, Harpo : this bike is fantastic - and all parts seem to be original:
The lamp-bracket, the front brake assembly , fenders + fender brackets are all special Schladitz-design - nothing has been changed. Great

You also did a great job in preserving the lady - no overpolishing, just cleaning and maybe some wax (?)...
I also have a Schladitz and I like them in particular for their unique method of adjusting the main bearing /bottom bracket :
Many German bicycles had a "Glockenlager" ; direct translation="Bell Bearing" where "bell" is refering to the prolonged cup on the pedal arm which reaches a small portion over the bottom bracket.
This "Glockenlager" came up around 1900 and was a big hype - the bell-cover was supposed to hold dirt away from the ball bearing and gain "engen Tritt" (="Narrow Tread"), by bringing the balls of the bearings further to the center, inline with the chain-line.
The downside of this design is the method of attaching the crank arms to the main spindle by means of a press fitting:
A tapered pocket on the crankarm is pressed onto the tapered shank of the main spindle. This assembly is very hard to dismount, espeically after may years of corrosion.
In my eyes this is a big disadvantage and the simple, old "Safety Style Cotter Pin" was much better -
but a forged taper and smooth cups were a lot cheaper to manufacture compared to milled keyways, thread cutting in bottom brackets and cups, or all these other fancy designs.
So long story short:
Many German bikes had these Glockenlager and to adjust the bearing slack is was necessarry to remove the left pedal arm to access the cone and locknut for adjusting the spindle-play. Without a special tool you can only jam off the pedalarm with a big hammer and many times this was (is) fatal.
So Schladitz went a different way with their Glockenlager:
You can adjust the play from the outisde and secure it with a littkle screw that reaches through the pedal arm.
This ingenious method was not only used by Schladitz and Mars (Nurenberg), but I was very amazed to see it on my Pierce Full Suspension as well
Your Schladitz is from the early Twenties:
source: fahradsammler.de
Here are a few photos of mine:
In case you need advice for servicing the bottom bracket (Removing the cranks) , just let me know - there is a very good and safe method.
You need 28" x 1 1/2 tires with beaded edges (Wulstreifen) -
Colored in red and black is no problem - you can still buy them (I stocked 5 red pairs at home, in case they run out like the white ones did last year

... If you need help, just let me know.
I'll see if I can find a catalog-scan of your machine...
By the way: your Schladitz-Albina was out of the less pricy line-up - you can compare it to the Hartford-machines which Columbia offered to satisfy customers who wanted "Columbia-quality" for a lesser price.
Good night
Jochen