Revisit all the public methods in TaskManager, ExecutionGraph and ExecutorManager

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1. Make sure all the public methods are necessary to be public
2. Clearly define and document what kind of Errors could happen.

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Start by reading the public methods in TaskManager, ExecutionGraph, and ExecutorManager. Determine which methods need to remain public and document the kinds of errors each can produce. Done means the public API has been reviewed and its error behavior is clearly defined.

Written by the indexing model from the issue text.