I have the below requirements where workflow is required:
My confusion is whether to integrate a workflow engine for this or not -
If yes, which workflow engine will support this flow.
If not, should I go around and build a custom workflow engine and a UI as per my needs or there's a better solution?
You could take a look at unify-flowret, a lightweight Java orchestration engine I created as part of developing a new platform in American Express.
Here are the core features. Very simple workflow definition, state management, parallel processing, comprehensive audit logging, ticket management, process variables, call back life cycle events, crash resilience, SLA and work management etc.
You can checkout unify-flowret at https://github.com/americanexpress/unify-flowret.