I am researching schools for the wealthier children in the 1880s and I realized I couldn’t find anything on the discipline system from that time period. Did they have detentions? Did they use demerits? Did they have permenate records that recieved black marks? Were physical punishments used? Were they made to clean/cook/assist teachers? It would be great if somebody could help with this question.

In Britain in the 1880s the most common punishment was corporal punishment, usually with a cane. Six strokes was the maximum allowed, and the punishment had to be recorded in the punishment book. The other punishments you mention are more recent in origin. These days corporal punishment is banned, and the raft of lesser punishments are not always effective!