With POP3 configuration you download the messages to your computer.
If you setup K-9 Mail on your phone you get the messages straight from the server.
So there is no synchronise with your computer.
With POP3 configuration messages that you already have read on your computer will show as unread on your phone. This is how POP3 works.
If you want to use your phone without Google, have a read switch to open os now-why-how