Opening your timetable…
When your timetable changes in Outlook, export the calendar again and load the new calendar.ics here. It's saved to your account, so your phone and your Mac both switch to it. Your attendance ticks are kept separately, so they survive a reload of the timetable.
Your ticks and any calendar you load are saved to your account, so every signed-in device shows the same thing. Once a device is signed in it stays signed in for good, until you sign it out here or change the password.