>Is a working phone number required to create an account there?

No, you can sign up with just an email address assuming you don't look like a bot.

Recently singed a family member up, and set up a couple of accounts to follow, ect. It worked for less than a day before the account was "locked", and the only way to unlock was to add a phone number.

As far as I'm considered, Instagram absolutely needs a phone number. Officially they don't need one at sign up - but they won't allow you to use that account for long before you need a phone number anyway.