How to be invisible on whatsapp?
There are apps that get around the limitations you mentioned, and they're able to retrieve the messages without you opening WhatsApp.

There are many similar apps on the play store, one of them is called private read for WhatsApp it displays the messages and media in it's own app without you having to open WhatsApp, this way you can view the content without the other person knowing. I've never tried the app, and so I cannot vouch for it's accuracy.

As for hiding the fact that you are online while using Whatsapp, you should first disable your last seen from WhatsApp settings, and then, every time you want to open WhatsApp, you should put your phone into airplane mode. That way no-one will be able to see that you're online. (The messages will be sent after you exit WhatsApp, and go out of airplane mode)