Matruchus: It seems your graphic driver my not be working correctly. Which graphic card do you use? The black screen is definitely a driver issue as much as I know.
The boot screen with Linux types is normal. If you installed it correctly it should also have Windows 10 boot launcher listed there.
Adding to
Matruchus's reply, generally new Linux installations need some tweaking.
Maybe the GPU drivers are not installed and you need to install them.
On the other hand proprietary GPU drivers are not enabled by default, even if they are installed. Type "Driver Manager" into the Cinnamon's menu search box and select the appropriate drivers if available.
For the black screen hang during shutdown, maybe your system logs could help (open "Log File Viewer" on Cinnamon).
Does the system restart/halt properly from the command line?
restart command:
sudo shutdown -r 0 halt command:
sudo shutdown -h 0 Also firewall on Mint is disabled by default. The easiest way to control it, is by installing a GUI (open package manager and search for gufw).