Database backup using RMAN
As far as I know, running a database in archivelog mode, backup is taken at short intervals, which I don't prefer.


No, archivelog mode and backup frequency has nothing to do with each other. Its you who defines the backup intervals. 


  I need the backup to be taken only once in a day, that too without shutting down my database. Is that possible?


No, it's not possible to take hot backup in noarchivelog mode.


  You can only backup a database in NOARCHIVELOG mode when the database is closed and in a consistent state. 


-Oracle Documentation.


  Which is better option, database to be run in archive mode or noarchive mode?


Oracle recommends to put your database in archivelog mode. There are chances that you may lose data in case of media or disk failure. 


  Also, if I'm going for noarchive mode, do I need to delete the backups manually or, does it happen automatically?


You need to take care of it, no matter whether you are operating on archivelog mode or noarchivelog mode. However, you can define backup retention policy

Documentation:
Configuring the RMAN Environment
Introduction to Backup and Recovery