A topic I'm always delighted to write about! I've answered similar questions about American schools so I'll be pulling from those answers. To the second part of your question, public education in the 1910s was fairly chaotic in general, especially in the American south. The first few decades of the 20th century saw the convergence of a number of policy and funding shifts that would eventually lead to the modern structure of tax-payer funded school districts and the expectation that children would spend their day in the company of other children, under the supervision of adults they weren't related to. These shifts included the passage of anti-child labor laws as compulsory school attendance laws moved from being laws in theory to laws in practice, the merger of schoolhouses into school districts with attendance boundaries, and the creation of funding structures that linked a school's budget to the count of children attending the school. It's possible some schools elected to hold children back a grade but generally speaking, grade retention was fairly uncommon and students moved through all 8 years (kindergarten was only just beginning to take shape and a high school diploma wasn't yet an essential criteria for adulthood) fairly unencumbered.

These shifts, plus the solidification of the modern liberal arts curriculum, happened across the country at difference rates and meant that what happened at school (or college) during the Spanish Flu was highly, highly dependent on local context.

First, to colleges. From an older response:

One thing to establish is that in 1918, attending college was a fairly uncommon event in a young person's life. According to the NCES, there were 1,041 designated institutions of higher education in 1918. By 1992, there were 3600. Also according to NCES, 3.4% of 18 to 24-year-olds were enrolled in college in 1917-1918, 4.7% in 1918-1919. By 1991, the percentage was up to 51% (but also, in 1990, 44% of enrolled students were over the age of 24.) In contrast, there were hundreds, if not thousands of schools in some cities and states as districts were only just beginning to merge.

In addition, Fall semester of American colleges doesn't nearly track onto the Fall months. Many colleges of the era started in mid to late-August and ended after Thanksgiving or in mid-December, meaning young people arrived during a lull in the pandemic while others were attending college near where they lived. It's safe to say everything that happened at universities during the pandemic was fairly idiosyncratic. However, we can see a few patterns and it looks like most colleges made the call to quarantine sick students, require masks, and teach outdoors when possible.

Genevive Carlton did a nice round-up here of different moves at different colleges. Her findings are interesting and speak to what was happening around the country:

Stanford was hit hard by World War I, which impacted how the college operated University of Montana held classes in the open University of North Carolina went into lockdown and quarantined as many students as possible, with limited success "At Elon College, the influenza epidemic struck in mere days, spreading to 75% of the students. With no time to close campus, the college transformed its gym into a makeshift infirmary, with healthy students nursing those who fell ill." One thing that I think can't be separated from the pandemic is the impact of World War I on student populations. It looks like there was a policy for closing schools due to Student Army Training Corp activities, concurrent to the flu so it's possible there were schools that closed for the activities, which helped reduce the spread.

From the K-State Collegian on Oct. 18, 1918:

The Aggie football schedule has been interrupted to quite an extent due to the epidemic of the Spanish influenza. The Aggies have been unable to carry out their schedule this season, because of the orders of military authorities, which forbade teams in a valley school where there is an [Student Army Training Corp training] to leave their school for more than a day. The closing of the schools throughout the valley has likewise made it impossible to schedule games with teams within one day‘s traveling distances.

It had been planned by Coach Clevenger to have Kansas University here this Saturday for a game, but the closing of the school made it necessary to cancel this game. It is currently being planned to schedule a game for a week from Saturday here with either Kansas University, the Haskell Indians or Washburn. A page from the 1918-1919 Royal Purple Yearbook about the "Big Five" - the players expected to lead the team for the season limited by the formation of the Student Army Training Corp and eventually, the Spanish flu epidemic.

Only one Aggie starter has been in the hospital, and it was reported this afternoon that is was fullback Azel Husted. Husted has been quite ill during the past week, but is now starting to improve and is expected to be out of the hospital within the next few days.

With regards to K-12 schools, a lot came down to teachers' health but again, each school/district/city handled it a little bit differently. Boston stayed open, NYC closed. Meanwhile, I found multiple instances of short notices in local papers announcing that school would reopen or had reopened following the Christmas holiday because the teacher no longer had the flu. One listing read simply:

Centennial school in Hamilton township opened on Monday. The teacher, Miss Minnie Coble, has recovered from the flu.

Most of the re-opening notices that I found appeared to be clustered around January, 1919 but there were multiple instances where a school announced re-opening in the Fall of 1918 after a short closing and a second re-opening announcement appeared in December 1918 or early 1919.

Some schools did try to stay open during the pandemic but faced resistance from teachers. In November 1918 while the Anne Arundel County (Annapolis, Maryland) County Health Advisor was announcing that schools were going to open, a group of teachers in Pennsylvania refused to go to work as some of their colleagues had gone to a conference and contracted the flu. By August and September 1919, Spanish Flu had pretty much burned itself out and schools opened normally.

In this longer answer, I get into more about cleaning routines and procedures but one thing that's worth stressing is that part of the responding to the Spanish Flu was responding to the deaths of hundreds of children. From the piece:

To us in the modern era, it can be overwhelming to look at the statistics around the Spanish Flu (195,000 American deaths in just October 1918) and have difficulty connecting to the human impact. While looking for articles about schools' responses to the Spanish Flu, I came across dozens of funeral notices in local papers for children who died, even some from families that lost multiple children in one week or day. School can sometimes feel like an impersonal space but those notices serve as a reminder that the adults working in them have long tried to do what they feel is best for the children they're responsible for, making the best decisions they can with the information they have.

Although there's limited evidence of specific day to day practices in schools of the era, we do know that teachers had to deal with the losses and help their students through that loss.