Can anyone briefly explain these commerce cloud concepts?
Is there a free trial version of commerce cloud available? If yes where can I find it? How can I enable commerce cloud in my Developer Org?
Commerce Cloud is what was formerly branded as Demandware that Salesforce recently acquired. To the best of my knowledge, it isn't yet available for enablement in a Dev Org. You'll want to contact your Account Rep to ask about a trial.
To answer your other questions:
Commerce Cloud is intended to provide a personalized customer-centric engagement as they shop. It allows service agents to offer relevant suggestions, answer questions and interact with shoppers, plus provide knowledge articles, answer questions, etc. The analytics included are extensive. Its architected to provide security for shopping/checkout, catalog, site and inventory management features that can be integrated with your Salesforce instance for your other business purposes.
The specific infrastructure used to host Customer Data is described in the “Infrastructure and Sub-processors” documentation available here.
For options, see your Account Representative. I'm only aware of one "version".