See if there is a setting (Softaculous or WordPress) for "rotating" the backups and how often. It should only keep the last X backups and unless your site changes a lot, you shouldn't make backups too often.
1. You should download your backups. If something happens to the server or your account, what good are the backups if they are stored on the account?
2. If you cannot find the "rotate" option, yes, delete all but the last backup on the server. That way if you just want to go back to last weeks version, it will be there. Anything older should be stored on your home computer.