Using psql, how to test if I am using streaming, hot_standby or warm replication?
Streaming does use WAL.  It obtains the WAL by streaming it, rather than (or in addition to) shipping entire WAL files at a time.  Also, the choice of hot_standby versus warm standby is independent of the choice of streaming versus log shipping.  It would be unusual to use hot_standby without also using streaming in the modern age, but it is perfectly possible to do so.

On the master, you can see if there are active receivers of WAL streaming by looking at pg_stat_replication.  If there are no entries, than no one is currently streaming wal.

For log shipping, you can look in archive_mode.  If that is turned off (or if it turned on but archive_command is some dummy command), then no one can be receiving the shipped log files as they are not being archived in the first place.  If it is on and archive_command is sensible, then someone might be doing something with the archived logs files.  The master server has no direct way of knowing whether someone is or is not.

In either case, the master doesn't generally know what they are doing with WAL.  They could be using the WAL for warm standby, they could be using it for hot standby, they could be storing it cold for future use, they could be just tossing it in the trash. Some of the fields in pg_stat_replication can give you some clues about what is going on, but who knows, the client programs might be lying.  And for log shipping, there is no way to know anything.