Given your page setup, I think this will be very difficult if not impossible with Axure. There is no way I’m aware of in Axure to change anything on a different browser window instance, whether it is a popup window, another tab or another browser instance. While you can open new browser windows, you can’t target them, and they have their own separate global variable “space” so no way to update or reload an existing browser window that is separate from your initial browser window. I suppose you could set up a frameset and then target the other 2 frames, but this would look and behave differently than what you describe here. I’m not aware of a way to do this in any web language/platform without a connected server-side system–and that would be way beyond straight prototyping. If you have web developer help, ask them though.
My recommendation is to place all the content of your 4 pages onto Page 1, with a different dynamic panel for each page.
Faking a popup window in this manner is pretty easy–just show the “Page 2” dynamic panel (and you can even fake the browser popup “chrome” by taking a screenshot of a blank popup window and place that image behind your “Page 2 Content” dynamic panel, or in the background of each dynamic panel state for “Page 2 Content.”
Faking a new/different browser tab takes a little more planning, and has a key limitation. When I’ve done something similar I needed to fake the entire browser and set the “real” browser to fullscreen mode. Essentially you would have an “outer” dynamic panel for each tab (Tab 1 with Page 1, and Tab 2 with an “inner” dynamic panel: State1 for Page 3 and State2 for Page 4.) Take a screenshot of a browser with one tab and another with two tabs open. Create hotspots over the “tab buttons” so clicking them changes the outer dynamic panel state–thus showing the “other” tab. You can keep Page 2 as its own separate dynamic panel.