For permissions, you can read about the ACLs here -> https://hyperledger.github.io/composer/reference/acl_language.html
'Composer Network' represents the business network entity. 'Composer Identity' refers to a specific blockchain identity that is mapped to a single Participant - defined in a Participant Registry that is contained within the business network in question.
Registries maintain a particular type of view of an Asset, Participant . Registries are also maintained by Composer for Identity or Historical transactions. It allows someone in that business network (given the right authority) to see the current status and history of the ledger, and Registries classify that much like a database table might do - ie depends on the level of details required (eg. Backroom Traders (Participant), Front Office Traders (Participant), Metal Commodities (Assets), Agricultural Commodities (Asset) etc etc) - or could just be rolled up as 'Traders'(Participant) and 'Commodities' (Asset) types if less detail is required. The salient point is you store Participant - or Asset Instances - in their respective type registries.
See the tutorials for examples of Assets and Participants in action: