Explanation
The hierarchy is, from top to bottom: Job, Stage, Task.
Executors and slots facilitate the execution of tasks, but they are not directly part of the hierarchy. Executors are launched by the driver on worker nodes for the purpose of running a specific Spark application. Slots help Spark parallelize work. An executor can have multiple slots which enable it to process multiple tasks in parallel.

Explanation
Output of correct code block:
+---------+-------+
|predError|storeId|
+---------+-------+
| 3| 25|
+---------+-------+
This question is difficult because it requires you to understand different kinds of commands and operators. All answers are valid Spark syntax, but just one expression returns a single-row DataFrame.
For reference, here is what the incorrect answers return:
transactionsDf.filter((col("storeId")!=25) | (col("productId")==2)) returns
+-------------+---------+-----+-------+---------+----+
|transactionId|predError|value|storeId|productId| f|
+-------------+---------+-----+-------+---------+----+
| 2| 6| 7| 2| 2|null|
| 4| null| null| 3| 2|null|
| 5| null| null| null| 2|null|
| 6| 3| 2| 25| 2|null|
+-------------+---------+-----+-------+---------+----+
transactionsDf.where(col("storeId").between(3,25)) returns
+-------------+---------+-----+-------+---------+----+
|transactionId|predError|value|storeId|productId| f|
+-------------+---------+-----+-------+---------+----+
| 1| 3| 4| 25| 1|null|
| 3| 3| null| 25| 3|null|
| 4| null| null| 3| 2|null|
| 6| 3| 2| 25| 2|null|
+-------------+---------+-----+-------+---------+----+
transactionsDf.where(col("value").isNull()).select("productId", "storeId").distinct() returns
+---------+-------+
|productId|storeId|
+---------+-------+
| 3| 25|
| 2| 3|
| 2| null|
+---------+-------+
transactionsDf.select("productId", "storeId").where("storeId == 2 OR storeId != 25") returns
+---------+-------+
|productId|storeId|
+---------+-------+
| 2| 2|
| 2| 3|
+---------+-------+
Static notebook | Dynamic notebook: See test 2

Explanation
The cluster manager allocates resources to Spark applications and maintains the executor processes in client mode.
Correct. In cluster mode, the cluster manager is located on a node other than the client machine. From there it starts and ends executor processes on the cluster nodes as required by the Spark application running on the Spark driver.
The cluster manager allocates resources to Spark applications and maintains the executor processes in remote mode.
Wrong, there is no "remote" execution mode in Spark. Available execution modes are local, client, and cluster.
The cluster manager allocates resources to the DataFrame manager
Wrong, there is no "DataFrame manager" in Spark.
The cluster manager schedules tasks on the cluster in client mode.
No, in client mode, the Spark driver schedules tasks on the cluster - not the cluster manager.
The cluster manager schedules tasks on the cluster in local mode.
Wrong: In local mode, there is no "cluster". The Spark application is running on a single machine, not on a cluster of machines.

Explanation
Correct code block:
importedDf = spark.read.json(jsonPath)
importedDf.createOrReplaceTempView("importedDf")
spark.sql("SELECT * FROM importedDf WHERE productId != 3")
Option 5 is the only correct way listed of reading in a JSON in PySpark. The option("format", "json") is not the correct way to tell Spark's DataFrameReader that you want to read a JSON file. You would do this through format("json") instead. Also, you can communicate the specific path of the JSON file to the DataFramReader using the load() method, not the path() method.
In order to use a SQL command through the SparkSession spark, you first need to create a temporary view through DataFrame.createOrReplaceTempView().
The SQL statement should start with the SELECT operator. The FILTER operator SQL provides is not the correct one to use here.
Static notebook | Dynamic notebook: See test 2

Explanation
Reroute a query in case of an executor failure.
Correct. Although this feature exists in Spark, it is not a feature of Adaptive Query Execution. The cluster manager keeps track of executors and will work together with the driver to launch an executor and assign the workload of the failed executor to it (see also link below).
Replace a sort merge join with a broadcast join, where appropriate.
No, this is a feature of Adaptive Query Execution.
Coalesce partitions to accelerate data processing.
Wrong, Adaptive Query Execution does this.
Collect runtime statistics during query execution.
Incorrect, Adaptive Query Execution (AQE) collects these statistics to adjust query plans. This feedback loop is an essential part of accelerating queries via AQE.
Split skewed partitions into smaller partitions to avoid differences in partition processing time.
No, this is indeed a feature of Adaptive Query Execution. Find more information in the Databricks blog post linked below.
More info: Learning Spark, 2nd Edition, Chapter 12, On which way does RDD of spark finish fault-tolerance?
- Stack Overflow, How to Speed up SQL Queries with Adaptive Query Execution