Data Velocity is an essential factor in determining the choice between batch and real-time processing in Hadoop applications. It refers to the speed at which data is generated and the need for processing it in real-time or in batches based on the application requirements.

For complex data processing tasks in a Hadoop environment using Python, PySpark is the most suitable library. PySpark provides a Python API for Apache Spark, allowing data scientists to leverage the power of Spark for distributed and parallel processing of large datasets.

Garbage Collection is a recommended practice in Hadoop for efficient memory management. It involves automatic memory management by identifying and freeing up memory occupied by objects that are no longer in use. Proper garbage collection enhances the performance of Hadoop applications.

You would leverage Avro for storage and Parquet for querying in a Hadoop environment with high query performance requirements. Avro's fast serialization is suitable for write-heavy workloads, while Parquet's columnar storage format enhances query performance by reading only the required columns.

In a Hadoop cluster, the NameNode acts as the master. It manages the metadata and keeps track of the location of data blocks in the Hadoop Distributed File System (HDFS). The NameNode is a critical component for ensuring data integrity and availability.

In Apache Oozie, Decision actions allow conditional control flow in workflows. They enable the workflow to take different paths based on the outcome of a condition, providing flexibility in designing complex workflows.

In Hadoop, YARN (Yet Another Resource Negotiator) plays a critical role in scheduling and coordinating workflow execution in data pipelines. YARN manages resources efficiently, enabling multiple applications to share and utilize resources on a Hadoop cluster.

Advanced cluster monitoring in Hadoop involves analyzing log files for predictive maintenance and optimization. Log files contain valuable information about the cluster's performance, errors, and resource utilization, helping administrators identify and address issues proactively.

Hadoop operates on the principle of "Data parallelism," which enables it to process large datasets by dividing the workload into smaller tasks that can be executed in parallel on multiple nodes.

The 'V' that refers to the trustworthiness and reliability of data in the context of Big Data is Veracity. It emphasizes the quality and accuracy of the data, ensuring that the information is reliable and trustworthy for making informed decisions.

Apache Pig uses a dynamic schema approach in data processing. This means that Pig doesn't enforce a rigid schema on the data; instead, it adapts to the structure of the data at runtime. This flexibility allows Pig to handle semi-structured or unstructured data effectively.

In Hadoop, Failover mechanisms are implemented to automatically recover from a node or service failure. These mechanisms ensure the seamless transition of tasks and services to healthy nodes in the event of a failure, enhancing the overall system's resilience.