DBMS_JOB is an interface to the Administrative Taks Scheduler (ATS) of Db2-LUW for the sake of some compatibility with Oracle RDBMS. However, you can also use the ATS directly independently of DBMS_JOB, via ADMIN_TASK_ADD and related procedures.
My experience is that db2acd (the process that implements autonomic actions including the ATS) is unreliable especially when ulimits are misconfigured, and it silently won't run jobs in some circumstances. It also has a 5 minute wakeup to check for new jobs which can frustrate, and it requires an already activated database which is inconvenient for some use cases.
I would not recommend usage of the Db2 ATS for application layer functionality. Full function enterprise schedulers exist for good reasons.
For parallel invocations, I would use an enterprise scheduling tool if available, or failing-that use the scheduler supplied by the operating system either on the Db2-server or at worst on the client-side, taking care in both cases that each stored-procedure-invocation is its own scheduled-job with its own Db2-connection.
By using a Db2-connection per stored-procedure invocation, and concurrently scheduling them, they run in parallel as long as their actions don't cause mutual contention.
Apart from the above, I believe the ATS will start jobs in parallel provided that the job-defintions are correct.
Examine the contents of both ADMIN_TASK_LIST and ADMIN_TASK_STATUS administrative views, and corroborate with db2diag entries (diaglevel 4 may give more detail, even if you must use it only temporarily).
Calls to SQL PL (or PL/SQL) stored procedures are synchronous relative to the caller, which means that the Db2-connection is blocked until the stored procedure returns. You cannot "make the session accessible" if it is waiting for a stored procedure to complete, but you can open a new connection.
Different options exist for stored procedures that are written in C, or C++, or Java or C++/CLR. They have more freedom. Other options exist for messaging/broker based solutions. uch depends on available skillsets, toolsets, and experience. But in general it's wiser to keep it simple.