how to make yahoo mail (Rogers) appear as unread after mail.app gets it

What you have provided is not the way it works with my IMAP account and POP account that I access with the Mail.app on my Mac and with the iPhone's Mail client.

Although it is possible to access a POP account with more than one email client, a POP account is designed to be accessed with a single email client only. The account's Inbox mailbox with a POP account is not kept synchronized with the server as with an IMAP account. With an IMAP account, if you read a received message with the email client on your computer, the received message will be available when accessing the account's Inbox mailbox with the iPhone's Mail client but will be marked as read and vice-versa since the account's Inbox mailbox with an IMAP account is kept synchronized with the server automatically along with all other server stored mailboxes. With a POP account, all new messages received at the incoming mail server will be downloaded as new unread messages with each email client used to access the account.

Since a POP account is designed to be accessed with a single email client only, only one email client can check the incoming mail server for new messages and download new messages received at the incoming mail server at a time. If a 2nd email client checks the incoming mail server for new messages while another email client is doing the same and/or downloading new messages, the 2nd email client will be temporarily locked out by the incoming mail server. This should not prevent a 2nd email client from downloading new messages received at the incoming mail server when another email client is not doing the same.

When creating a Yahoo account with the iPhone's Mail using the Yahoo account preset, the account is created as an IMAP account, but Yahoo does not support accessing a Yahoo account as an IMAP account with any other email client. You can't access the account as an IMAP account with an email client on your computer - you must access the account as a POP account. Accessing an account as a POP account with one email client and as an IMAP account with another email client can cause problems.