Is it safe to restart PostgreSQL if process terminated for some reason?
Postgres generally handles server restarts pretty well.  Assuming that all the correct hardware is in place (battery-backed cache, etc.), bringing up Postgres after a crash will automatically cause it to enter recovery mode, where it will attempt to replay all the WAL files since the last CHECKPOINT.  Once it has finish replaying up to a consistent state, you are free to use the database and continue with your business.  Having said that, however, it's up to you as the DBA to perform consistency checks as per your business requirements to ensure there is no corruption.

Disclosure: I work for EnterpriseDB (EDB) as a Support Engineer