The GQQ001A message indicates that a task is trying to obtain a lock on a PDS file that is currently locked by another task. The correct procedure is to enter EOB, this will cause the task to wait and then retry the lock. If no other message is displayed all is good, the lock has been released and the task has continued processing.
There is only a problem if the GQQ001A message is issued repeatedly. This may indicate that the task holding the lock has abended and left the lock in place. At this stage you should inspect the cpuid and taskid in the message and determine whether the owning task is still active.
It appears that in your case the operators are correctly issung EOB and the lock is eventually being released.
The other problem you report is that jobs are not being submitted. You can see that PCS is scheduling the jobs, because the &SUB messages appear, but the jobs are not being sent from your CMS server. The fact that increasing the SHARE for the CMS server appears to resolve this would indicate to me that during times of high activity the CMS server is not being dispatched often enough to satisfy your scheduling requirements. We generally recommend giving the PCS CMS server a high priority, as it is not a very active machine, but when it is active it does need to respond quickly.