On the topic of week starts, US calendars is funny because it starts on Sunday. European calendars start on Monday. In some Muslim countries they have Fridays, Saturdays off, and I guess they work again on Sunday. Welcome to dealing with time! I'm sure you've also read:
https://infiniteundo.com/post/25326999628/falsehoods-program... . I guess a logical option would be to have 2 options: "Start week on [Weekday]" (using a dropdown chooser) and "Show [n] days" (some people maybe want a 6-day week, and others just a 3-day one!).
I noticed the "Copy" button generates a copy-pastable text. I was half expecting an encoded URL that one could share with people, they'd open this URL in their browser and see what the user just entered. For me at least it's easier to see a graphical calendar rather than trying to parse entries like "Friday May 1, 8:00-10:00."
The data doesn't even have to be stored server-side, you could encode the times and generate a URL with a "#", which the app would then decode so it could render the calendar with the markings.