Do the message ID’s in my POP3 mailbox change if I delete one of them?

No, the message ID’s do not change. At least, not right away.

Pop3 marks the message for deletion which will occur as soon as the connection is broken.

For example: If you have 10 messages in your mailbox with ID’s ranging from 1 to 10 and you delete message ID 5 all other ID’s stay the same.

You will have the following valid Message ID’s: [1..4] and [6..10].