1. Something like that, yeah. It's a lot like Civilization, with magic. Or Age of Wonders, or Master of Magic, if you've played those.
2. You get into the beta if you order from Stardock directly (ie: through the Impulse website). It doesn't matter if you order a digital or physical version.
3. I'm not sure if the current cycle is still open or not. If it is, you'd get in immediately. If it's closed, your pre-order would get queued up and you'd get in once beta 2 starts.
Also keep in mind that this is a real beta, not a demo. It's not fun. It crashes. Many things don't work or aren't implemented yet. It's great if you want to give feedback because you can do so at a relatively early stage of development (where its easier to change things).
But if you're looking to just play and have fun, you don't want this beta. 