For real-time data syncing between Hadoop and RDBMS, Sqoop can be integrated with Apache Kafka. Kafka enables the seamless and real-time transfer of data between Hadoop and relational databases, supporting continuous data integration.

Apache Pig's optimization mechanism is crucial for efficiently processing large volumes of data. It includes various optimizations like predicate pushdown and filter pushdown to enhance the performance of Pig scripts.

In scenarios where data processing efficiency is crucial, MapReduce is often the most effective Hadoop programming paradigm. It excels at processing large datasets in a distributed and parallel fashion, making it suitable for scenarios prioritizing efficiency over real-time processing capabilities.

In a Hadoop cluster, Zookeeper Nodes are crucial for maintaining continuous operation and data accessibility. Zookeeper is a distributed coordination service that helps manage and synchronize distributed systems, ensuring the coordination of tasks and maintaining cluster stability.

To address the 'Small Files Problem,' a Hadoop administrator can use CombineFileInputFormat. This technique allows the efficient processing of small files by combining them into larger input splits, reducing the overhead associated with managing numerous small files and improving overall processing efficiency.

Capacity Planning is used to estimate the processing capacity required for a Hadoop cluster based on data processing needs. It involves analyzing factors like data volume, processing speed, and storage requirements to ensure optimal cluster performance.

Hadoop's ResourceManager is responsible for resource allocation and management in the cluster. It assists in monitoring cluster performance by efficiently allocating resources to applications, ensuring optimal utilization and performance. This includes managing memory, CPU, and other resources for running tasks.

Apache Spark performs computations in-memory, which is a key improvement over the MapReduce model. This in-memory processing reduces the need for intermediate disk storage, resulting in faster data processing and analysis.

Impala's in-memory processing feature enables it to store and analyze data in memory, providing faster query performance and real-time data analysis capabilities in Hadoop clusters.

Data Serialization is a critical factor in Hadoop Streaming API when dealing with streaming data from various sources. Proper serialization ensures that the data is efficiently encoded and decoded, enhancing the performance of data processing in Hadoop Streaming.