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Very broadly speaking, yes. Most DC-compatible apps I know of are the same as, or forks of, their older server-based incarnations.
Simple core functionality in server and DC is pretty much the same, so apps that don't have complex needs will simply work. The most obvious ones are reports - they're simple flat reads of data and don't need to do anything that's affected by server or DC.
There's a nice list of things all DC developers need to think about on top of developing for server (albeit, some of them they should be thinking about for Server anyway) - https://developer.atlassian.com/platform/marketplace/guidelines-for-data-center-app-development/
(p.s. DC apps are always compatible with Server, unless someone found a good reason to code for "hey, work differently if there's only one node in the cluster")
Yes it should work but it's not recommanded. You may face stange behaviours on some app because it's not means to work in a cluster so you often face cache issues.
Please find Atlassian related kb below.
Regards
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