PostgreSQL / pgAdminIII: is it possible to send command line commands via the UI
If by "command line" you mean the client program psql, then the answer is no. psql is just another client program like pgAdminIII.

If you have configured File -> Options -> Browswer -> Binary paths -> PG bin path in pgAdminIII, there is a shortcut to open psql:





pg_dump is another separate client application. You run it from the shell of your OS. You don't "send it to Postgres". But you can optionally call it from within pgAdmin. See Tools -> Backup...

All commands starting with the shell prompt $ in Jay Taylor's answer are also commands to run in the shell. Be sure to connect to the right DB.