When dealing with time-series data in Hadoop, the optimal combination for performance is using the Parquet file format with Snappy compression. Parquet is columnar storage, and Snappy provides fast compression, making it efficient for analytical queries on time-series data.

For optimal results in aggregating data from multiple sources with Hadoop Streaming API, the approach should involve using Combiners for Intermediate Aggregation. Combiners help reduce the amount of data transferred between mappers and reducers, improving overall performance in the aggregation process.

In scenarios involving large-scale data aggregation, Apache HBase would be a suitable tool. HBase is a NoSQL database that provides real-time read and write access to large datasets, making it effective for quick data retrieval in aggregation scenarios.

Sqoop's incremental import feature benefits data ingestion in Hadoop by avoiding data duplication. It allows for importing only the new or modified data since the last import, reducing the amount of data transferred and optimizing the ingestion process.

Sqoop can be integrated with Shell scripts for custom data handling during import/export processes. This allows users to execute custom logic or transformations on the data as it is moved between Hadoop and relational databases.

Partitioning data in HDFS improves processing efficiency by enhancing data locality. This means that computation is performed on nodes where the data is already stored, reducing the need for extensive data movement across the network and thereby improving overall processing speed.

Snapshot recovery techniques in Hadoop allow for the restoration of data to a specific point in time. Snapshots capture the state of the HDFS at a particular moment, providing a reliable way to recover data to a known and consistent state.

Apache Hive is primarily used for building data pipelines involving SQL-like queries in the Hadoop ecosystem. It provides a high-level query language, HiveQL, that allows users to express queries in a SQL-like syntax, making it easier for SQL users to work with Hadoop data.

Apache Storm distinguishes itself in the Hadoop ecosystem by specializing in stream processing. It is designed to handle real-time data streaming and enables the processing of data as it arrives, making it suitable for applications that require low-latency and continuous data processing.

Ambari plays a critical role in managing and monitoring Hadoop clusters. It provides an intuitive web-based interface for administrators to configure, manage, and monitor Hadoop services, ensuring the health and performance of the entire cluster.