How best to parallel-processing such types of multiple similar query tasks?
This depends on how you are engaging with the queries when they return results. Let's assume you are running them from a programming environment with an ORM layer. In that case you can run each query in a separate thread and connection pipe, and the queries will run async just fine. If you are running at the command line using psql, you can just open multiple shells and run each query from a different shell terminal.
Postgres is very good at async queries, so your challenge is really figuring out how you will use the results of each query and setting up the environment sending the queries to perform asynchronously.