The ResourceManager in YARN architecture is responsible for allocating system resources to different applications running on the Hadoop cluster. It keeps track of available resources and schedules tasks based on the requirements of the applications.

Parquet is a highly efficient file format in Hadoop designed for fast data serialization and deserialization. It is columnar-oriented, supports schema evolution, and is optimized for both compression and performance.

A Hadoop administrator should prioritize data in different HDFS directories based on the replication factor. Critical data should have a higher replication factor to ensure availability and fault tolerance in the event of node failures.

Sink Groups is a key feature in Flume that allows for load balancing and failover among multiple sinks. It enables the distribution of events across different sinks, ensuring efficient load distribution and providing fault tolerance through failover mechanisms.

Data Replication is a critical factor in designing a disaster recovery plan for high availability in Hadoop. By replicating data across multiple nodes, Hadoop ensures that there are redundant copies of the data, reducing the risk of data loss in case of node failure. This redundancy enhances fault tolerance and supports disaster recovery efforts.

The Resource Manager in Hadoop cluster capacity planning plays a crucial role in resource allocation. It is responsible for managing and allocating resources across the cluster, ensuring that computing resources are efficiently distributed among different applications and tasks. This is essential for optimal performance and utilization of the Hadoop cluster.

High availability for the NameNode is achieved in advanced setups through an Active-Passive configuration. In this setup, one NameNode is active, while the other remains passive, ready to take over in case of a failure. This ensures uninterrupted NameNode services and minimizes downtime.

Avro is suitable for schema evolution due to its support for schema evolution. It allows for the addition of new fields and the evolution of existing ones without requiring modifications to the existing data. This flexibility is crucial in evolving data structures in a Hadoop environment.

The key advantage of using Crunch for data processing in a Hadoop environment is its provision of high-level abstractions. Crunch simplifies the development process by providing a higher-level API, making it easier for developers to express complex data processing tasks concisely.

Counters in Hadoop are used to monitor task progress. They provide valuable information about the execution of MapReduce jobs, helping developers identify bottlenecks, track the number of records processed, and troubleshoot performance issues during debugging.

The pydoop module in Python is commonly used for Hadoop integration. It provides functionalities to perform operations on the Hadoop Distributed File System (HDFS) and interact with Hadoop clusters using Python.

To troubleshoot connectivity issues between nodes, a Hadoop administrator should check the network configurations. It involves examining network settings, ensuring proper communication, and resolving any network-related problems that may impact the performance of the Hadoop cluster.