There's no point kicking inactive players out as you just hurt yourself (because you have to pay for someone else to join, and you get nothing back for kicking them out). I just ignore them pretty much.
As far as the cores, you need exactly 3 unsurged assets of different types around the core (not surrounding them, just do 1 of each). You're going to lose anything you have around the core when you surge it, so good to use cheap ones (buy the cheapest ones and upgrade them). If you have exactly 3, and it's not working, I'm not sure what's up.
I don't do multiples so don't know about any of that.