Declarative pipelines in Jenkins are designed for simplicity and readability. They provide a structured and concise syntax, making it easier to define and understand complex pipelines.

The Docker plugin in Jenkins allows the management of Docker containers within Jenkins jobs. It facilitates the seamless integration of Docker for building, packaging, and deploying applications.

Jenkins can be configured for rolling updates in a Kubernetes environment by using the Jenkins Pipeline with the rollingUpdate strategy. This allows for controlled and incremental updates to applications running in Kubernetes clusters.

The best practice involves using Shared Libraries to modularize and reuse parts of job definitions. Shared Libraries allow you to define common functionality and use it across multiple projects.

Jenkins can automatically poll source control systems like Git to detect changes in the source code. This enables Jenkins to trigger builds when changes are pushed to the repository.

The Node Management plugin is vital for managing and scaling Jenkins nodes in a distributed setup. It allows administrators to add, remove, and monitor nodes, ensuring efficient resource utilization.

In a parameterized build, the "Array" parameter type is used for accepting multiple string inputs. This allows users to input a list of values during the build process.

A Jenkinsfile is primarily used for defining the pipeline as code. It allows you to describe the entire build process, including stages, steps, and conditions, in a script format that can be versioned along with your code.

The use of a Dependency Manager can resolve conflicts in a Jenkins pipeline caused by dependency issues. It helps manage and resolve dependencies efficiently, ensuring a smoother pipeline execution.

Jenkins's integration with Kubernetes is key for automating deployments in a continuous delivery pipeline. Kubernetes provides container orchestration, allowing for efficient deployment, scaling, and management of containerized applications.