The default PostgreSQL listener. Applications connect here to run queries, and Postgres ships listening on localhost only, which is a sensible default worth leaving alone unless you have a specific reason not to.
Same rule as every database: not on the public internet. Postgres defaults to listening on localhost only, and that default is worth keeping.
Postgres reachable from the internet should be restricted to localhost or a private network. Review pg_hba.conf, since a permissive host rule is usually how it became exposed.
The port scanner will tell you whether 5432 is reachable on a host you control. Checking from outside your own network matters: a port can be open on the machine and still be blocked at the firewall, and it is the view from the internet that decides whether anyone else can reach it.
Only scan hosts you own or have permission to test.