Rangerat's advice is right on. I to encourage you to read this entire thread, the answers to your questions are here (probably page 15) and yes it will take a little time but you obviously have a little techie in you so go for it and learn something new....it took me days of googling to finally figure it out and this thread has the good info. Don't waste your time going back to 8, it is a clunky disaster, 8.1 is much better, think Win 7 with added features.
The Lenovo community may have your answer with updated drivers.
Start checking drivers in device manager--device by device-- sometimes there are flagged devices. If no flags start Disabling suspect drivers and shutting down until it doesn't hang on shutdown. Start with Bluetooth-LAN-WIFI. Systematically disable, test shutdown, then re-enabling and disabling and testing a few each time until you find the bad driver/s--- now UNINSTALL THAT DRIVER and when you reboot windows will want to find a driver to install... search windows 8.1 local-NOT THE INTERNET. 8.1 will (hopefully) find and install its own generic Microsoft drivers and the device is working.
Next go to the control panel and TURN OFF automatic updates. The problem is Automatic Updates will replace the generic driver with the device vendors bad driver -- that is why the problem comes back a day later. Set Automatic Updates to notify you when new updates are available and YOU check the updates (like a techie does) and Hide that update and wait until the proper update shows up.