Hi all, I am experiencing some problems too with the new spotlight, and I think I've found something interesting. I was running the iOS 9 GM on my iphone 5s and spotlight suggestions were working fine. Same thing on my macbook with the GM El Cap beta. Then I've installed the official release on the iphone and spotlight suggestions stopped working... while on wifi! Strangely enough they work fine when I'm on cellular.
Today I've updated my other machine (an iMac) from Yosemite to El Cap and spotlight suggestions as well as natural language input didn't work while on wifi. Inspired by the weird iPhone "bug" I've then connected the iMac to the internet through the iPhone on cellular via the hotspot function, and boom: spotlight suggestions started working properly on the iMac: web and wikipedia results, natural language and so on.
The weird thing is that I have this strange malfunction on an iPad, iMac and iPhone, while the macbook works fine even on wifi.
Maybe all of you who cannot make this work can do this quick test and check if the cellular connection suddenly makes spotlight suggestions work.
BTW For anyone who's keeping score: I'm located in Germany but my language and region settings are Italian and Italy.