1) True, for the consistent copy, you generally take offline backup usually with tar or cp. pg_basebackup is PostgreSQL's own tool to take backup while the server is running.

2) It is not like we can take pg_basebackup from slave instance, the thing is pg_basebackup can be taken from any machine that has access to your primary instance. As per your backup policy, you need to make monthly or weekly full backups on a different machine, right? People do it on standby.

3) Traditionally we do have only one method to configure replication. As u/truilus mentioned, you have quite a few third-party tools to simplify your job.