pg_dump is a logical export tuned for speed and multithreading. Almost certainly not what you want.
pgbackrest is the equivalent of BACKUP DATABASE and BACKUP LOG. It's an external program (stuffing everything in the database engine is not The Unix Way) which typically you run from cron. Redrirect stdout and stderr to a log file with a timestamp in the name. (That, at least, is what I've been doing for 8 years. It works perfectly.)
pgbackrest also has an "info" option which gives you details of all the backups currently in the repository.
> > Is there a way to see the restores performed on a database? > Is there an equivalent table to msdb.dbo.restorehistory in SQL Server? > Is there a way to implement an equivalent if one doesn't exist?
From what I understand there are various ways of doing this in SQL Server, which way are you interested in?
