I hope you realize that is all our fancy and not God speaking.
Sure, absolutely. I really don't know. I can't think of where God tells us of what a "day" in the life will be like in Heaven (as you go on to say). Whatever it is, I know I'll like it. :) We do know that God Himself is very busy in Heaven, having done many many things within time throughout history. We also know that the angels are busy. So, I have no problem in thinking that we will be also, in whatever form.
However, the Scripture tells us that we will be judged according to our deeds. And that means there will be eternal inequality as well.
We're probably at similar ends by different means. I don't think one can be "more saved" than the next guy in Heaven, but whatever "rewards" means will lead to inequality on some level. I don't even know if that suggests permanency. In any event it appears to me that we are purposefully left in the dark on these matters so our thoughts will be much farther away from doing works "to get that thing".
God finished His work by the 7th day. God does not exist in time. We don't know what God "does" in heaven. He is perfect and His work is perfect. Perfect means finished, complete. What is there 'left' for God to do. And, after the End of Times, with the new earth and the new heaven (why new heaven?), what will God do "then?"
Your anthropomorphism placeses a necessity on God to "do" something.