1) yes, you can tail or filter by date.
As easy as running
kubectl logs --help
Options:
-c, --container='': Print the logs of this container
-f, --follow=false: Specify if the logs should be streamed.
--include-extended-apis=true: If true, include definitions of new APIs via calls to the API server. [default true]
--interactive=false: If true, prompt the user for input when required.
--limit-bytes=0: Maximum bytes of logs to return. Defaults to no limit.
--pod-running-timeout=20s: The length of time (like 5s, 2m, or 3h, higher than zero) to wait until at least one
pod is running
-p, --previous=false: If true, print the logs for the previous instance of the container in a pod if it exists.
-l, --selector='': Selector (label query) to filter on.
--since=0s: Only return logs newer than a relative duration like 5s, 2m, or 3h. Defaults to all logs. Only one of
since-time / since may be used.
--since-time='': Only return logs after a specific date (RFC3339). Defaults to all logs. Only one of since-time /
since may be used.
--tail=-1: Lines of recent log file to display. Defaults to -1 with no selector, showing all log lines otherwise
10, if a selector is provided.
--timestamps=false: Include timestamps on each line in the log output
2) Docker stores the container logs in host in the path /var/lib/docker/containers/{ContainerId} so you could copy/truncate the logs directly.