MySQL Master Slave Replication and backup
Operations and issues on slaves will not impact the Master. I dont't understand your concept of "the master -> slave replication running every 5 minutes". All transactions on Master will immediatelty be replicate on slaves. 

If your tables are InnoDB, your dump will not lock any tables (with the option --single-transaction) so you can have normal activity on master and slave too. 

To backup your slave you can also stop the replication, shutdown your MySQL (Slave) and copy your datafiles or use a hot backup solution like Percona XtraBackup. 

Max.