When SOLAR reopens, do we expect to see the cores, labs, tutorials chosen based on what was assigned to us? And then modify from that? Or do we have to start from scratch building the schedule? I guess my main question is- do I have a better chance tweaking what I was given or building my ideal one?

You'll have been placed in cores, labs, and tutorials. You get to modify from that based on which ones still have seats available. Whatever you do - don't drop the classes and readd them or you'll lose your spot!

No, SOLAR will look almost exactly the same as when you left it, so you'll have much better chances "tweaking". You have set tutorials right now, and you'll have the option to choose form a list of available tutorials when you click "modify". If you don't get the tutorials you want now, just leave them the way they are and check again another day. Eventually the tutorial you want will open up (either from people dropping the course or people switching into other tutorials).