#1 We are working on adding a feature that will allow tracking the health of agents by looking at when they last polled the Prefect API for work from a work queue - you can follow the #announcements and release notes to stay up to date
#2 Good question. It depends on the infrastructure block. When you use KubernetesJob, DockerContainer or one of serverless containerized infra blocks, then flow run container or pod can run till completion even if agent that spun that up is down. But when you are using a Process block on a local server, then this flow run runs directly within the agent process and when your agent is down, the flow run cannot complete and you would need to delete this run e.g. from the UI if you are confused by the Running state. Usually such run would be marked as Crashed but sometimes Crashes may be hard to detect so feel free to open a GitHub issue and describe it in more detail if you see a different behavior than what I described and/or if this is still confusing