I was wondering if there is an API to access GAE's services including logs, performance, tasks in the queue, something like bulkloader.
There's no out-of-the-box way to access App Engine logs outside of your App Engine app (which you can do with the LogService API). However, there are examples, such as log2bq that export your logs into BigQuery.
Not sure what type of thing you're looking for here, but if the data is tracked via the logs, you can use the above example. If you can elaborate, perhaps I can better answer you.
You can use the TaskQueue REST API.
probably not, except there're several rest APIs to access queue tasks.