The first error is shown, in case a file did not finish harvesting yet but already falls under ignore_older. This can for example happen when a file is not updated anymore, but the harvester can't finish reading it as the output is not available or too slow. As soon as the output catches up, the file will be closed and ignored.
This brings us to the second errors: There seem to be some issues with the output which explains the first issue. As filebeat keeps retrying sending log messages on errors and you get all messages, it seems like these are some temporary connection issues.
Do you get any errors on the Logstash side?