1. System Databases subclient will pull system databases if they haven't been manually discovered elsewhere, all of the methods you mentioned are also valid, but also see using BackupAGDBsViaActualInstance below for possibly an easier way.
2. You can definitely do that if you like, but model should be relatively stable, so might not be necessary to run log backup. You can tell databases not in full recovery model to skip T-Log if this is easier and then schedule T-Log anyway.
Adding a 'System Database' subclient will automatically pull the System DBs (master, model and msdb) into it during the next backup operation. Note that this only works if the databases were not manually discovered under another subclient previously. If they were auto-discovered under the default subclient, then next backup should move them to the System Databases subclient.
See BOL: http://documentation.commvault.com/commvault/v11/article?p=18158.htm
Default subclient will backup up all available databases that are not otherwise discovered under user-defined subclients.
As of V11 SP11 (I believe) the databases currently discovered under your AlwaysOn Group client should be automatically skipped from backup under subclients on the stand-alone node, but if you're not seeing that occur you can look at implementing the BackupAGDBsViaActualInstance additional setting.
Before V11 SP11, this was only possible with a Global Additional Setting http://documentation.commvault.com/additionalsetting/details?name=%22BackupAGDBsViaActualInstance%22&id=
After SP11 this can be done on a per-client level: http://documentation.commvault.com/additionalsetting/details?name=nBackupAGDBsViaActualInstance
For more information on the AG client see: http://documentation.commvault.com/commvault/v11_sp13/article?p=18295.htm
Note: The client SP level is what determines whether the additional setting above needs to be set at theglobal or client level.
In terms of needing to run log backup for the model database, this database by rights should not be growing. It is just a template database from which all new databases (and TempDB) are created. If you do notice it growing you can definitely schedule log backup against the subclient.
Prior to V11 SP11 you can tell a backup to automatically skip transcation log backups on databases that in simple recovery model by checking the "Skip transactional log backups for simple recovery model databases"
From SP11 onwards the default behaviour is to skip transaction log backup on Simple Recovery model databases.
How you would like to configure the scheduling is up to you, but if you would like to run a t-log backup right after the full just to ensure truncation is occurring that would be fine.
One thing that's worht noting here, running a log backup does not shrink the physical file size on disk. If model has runaway (unlikely, but has been known to happen) you will need to run a shrink file on it after flipping recovery model on the database.
I hope this helps