Hi,
1. You are correct that while the Management API's can manage simple gateways, they do not have a REST API or CLI for clusters, and dbedit is till the way to go for automating cluster creations.
2. R80 Security Management is a platform change. The .C files which we all know and love to change are no longer the database, but rather just a dump during the policy installation process. Security Management data with R80.10 (all of it, including VSX and VS's and any object comes to mind) is managed and versioned on the backend with 2 databases and a logical process called CPM.
3. A misconception about Install Database: it doesn't actually install databases. It is relevant to synchronizing object names with the log server, so that when viewing logs, IP's will be translated to Check Point object names. It also updates the SmartEvent Automatic Reaction configuration. But nothing Management or Gateway-wise.
4. So to answer your question, to verify that your changes were added correctly, use "dbedit show".
Hope this helps.