For your question 1: This wouldn’t usually happen when using the IMAP trigger node - it opens a connection and then triggers whenever new mail arrives.
However, there could be a wait whenever the connection gets interrupted. You could configure your logging to see verbose output like this to verify this.
For your second question: That’s the default behaviour - it triggers for new, unseen mails and ignores other messages in your inbox (which could also cause the behavior from your first question when your email client is marking messages as seen automatically). You can customize this behaviour under Options → Custom email rules:
The node uses this module under the hood, so you’d need to familiarize yourself with the respective search functionality in case you want to adjust this behaviour.