Stud partition walls (first floor) are not typical in older houses, no.
Paramount, Stramit and 2 or 3" block typical partition walls 50's, 60's and 70's.
Stud first floor partition walls were not uncommon construction in houses late 1960's and onwards that I worked on. I worked for a housebuilder who preferred internal partition walls in 100mm blockwork and would include steelwork in larger houses to support first floor blockwork where walls didn't follow up from ground floor partitions. The point is sweeping generalisations can be dangerous.
If there is not a lintel above the doorway in wall A, can this wall be holding any weight? All that is present is the timber frame lining and the doorway comprises the entire width of wall A.
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