How does Blockchain as a Service (BaaS) work? I've been so entrenched in the world of cryptocurrencies that I'm confounded by how a Blockchain as a Service would work in the enterprise realm. 

Both Microsoft and IBM have BaaS offerings, advertising that it will change the way your business functions.

I'd like to know, in general, how a blockchain system is run in the enterprise. Several questions come to mind:


Who runs the nodes? 
How many miners are required? I'm assuming the hashpower your own enterprise systems could provide would not be substantial enough to have impenetrable security.
Who provides the hashpower? The BaaS provider, or your own network of computers? 
Since you are the owner of this blockchain, how is this more secure than just a regular (encrypted) database with strict access control?
What is the format of the data stored in these blockchains? Are they able to insert any custom data format and payload in each transaction, since it is a proprietary blockchain?
Besides security in the form of immutability, what other benefits does a blockchain in the enterprise provide?
Who runs the nodes?

It depends on the type of Blockchain network you referring to. Typically it is permissionless or permissioned. For the permissionless; anyone/ any organization can volunteer to run full nodes as long as they ready to allow spare computing and bandwidth resources. No incentive Nor reward for this service. In future respective Blockchain company /developers - they may consider for incentive/s or rewards. This would ensure  more and more nodes running at a given point in time. More nodes means more secure for the block mining and there by your secure transaction/s. In recent past, there has been significant drop in "running full nodes". This is a bit of concern.

In addition, permissionless P2P network no access control is needed. Ex. bitcoin/ ethereum supports X.509 certificates and SSL encryption to verify receivers’ identity and help prevent man-in-the-middle attacks. Besides, Blockchain security validate each new block and follow protocol proof-of-work/stake which guarding against the bad actors.