Q:

How do I check the number of tasks currently in the queue?

According to the Push queue in GAE there are a number of task request headers.
X-AppEngine-QueueName, the name of the queue (possibly default)
X-AppEngine-TaskName, the name of the task, or a system-generated unique ID if no name was specified
X-AppEngine-TaskRetryCount, the number of times this task has been retried; for the first attempt, this value is 0. This number includes attempts where the task failed due to a lack of available instances and never reached the execution phase.
X-AppEngine-TaskExecutionCount, the number of times this task has previously failed during the execution phase. This number does not include failures due to a lack of available instances.
X-AppEngine-TaskETA, the target execution time of the task, specified in milliseconds since January 1st 1970.

Is there a way to check how many tasks are already enqueued?

A:

Not from the headers, no. But you can use the QueueStatistics class to query that information.

