Although the show is likely taking some dramatic license around the particular school where the show takes place, what you're describing is mostly typical for a rural, Canadian schoolhouse during the late 1800's.

Having students assist with school upkeep was a routine part of the school year, in both Canada and the United States. The notion of a school district staff with people designated with particular tasks - such as a custodian, superintendent, principal, etc. - wouldn't become the norm until well into the 20th century. As such, the teacher was responsible for a great deal of work associated with the school. One way to deal with that work was to recruit children to assist. There are dozens of first hand accounts from teacher journals that speak to how teachers attended to the daily tasks of a school. Those accounts would also speak to how difficult it was to keep every child engaged for the entire day. Due to a lack of resources, older or more talented students would quickly move through all of the available resources. In some places, they'd help teach younger students while in others, they'd be given additional responsibilities in the schoolhouse. Some teachers used additional responsibility as punishment, some as reward. Some worked it into the curriculum and used small jobs as a way to teach industry and thoughtfulness.

Schools were, in fact, quite small and student enrollment would range from 1 or 2 children to several dozen, often requiring children stand along the walls during lessons. By the late 1890's, schools were beginning to consolidate into districts and it's possible that in some towns, older children went to one schoolhouse while younger children went to another but it depended a great deal on what the local educational and town leadership decided. Policies around uniforms were also linked to individual policy makers' decisions. As the notion of a standardized school experience with explicit policies that were routinely enforced wouldn't become the norm until the next century, each school was, in effect, idiosyncratic. There were school inspectors in most Canadian provinces in that era, but the position was often symbolic and more about data collection. If the province and region did have a requirement for children to wear uniforms, there was no real way to enforce the rule. Likewise, if a local school adopted a uniform policy, there was no one to really tell them they couldn't. That said, it's possible that the teacher who required children wear a uniform to school brought the idea from her training at a religious teacher preparation college which in many cases, did have set rules about what future teachers needed to wear but that would have been her decision.

Finally, with regards to cooling their milk in a stream, that's another detail that is also highly idiosyncratic. Going to school for a set number of years, a set number of days, and a set number of hours wouldn't be the norm for generations. It's important to stress that there was no social stigma attached to not going to school to speak of so if a child didn't go to school, it was neither here nor there. The notion of school lasting from 7 AM to 3 AM with a break for lunch at the school wasn't as typically as it would be by 1940 or so. Instead, children would more likely attend the morning or afternoon session, the winter or spring session. Bringing a lunch to school wasn't the norm for the era but it wasn't necessarily unusual.