I've been using the SP8 since Tuesday and it is by far the best Windows 2 and 1 I've used.
Enhancements over the Pro7+
13" display that is the best panel I've seen on a Surface
Slim Pen 2 with haptic feedback
2 TB4 ports allow for further upgrades and use cases...
It was the Connected Standby Power State introduced in Windows 8 - allows for always on connectivity while maintaining battery life. It's like your smartphone - it can be in a low power state and still receive notification and calls.
Open PC Settings - System - Storage and it will give you a breakdown of what is occupying your space, my guess is you'll find you have a large number of Temp Files (including previous versions of Windows) and then Apps and System.
It will walk you through deleting what you don't need.
Are these older applications? Some older application struggle on High DPI screens (like the Surface), you can attempt running the Application Troubleshooter Settings - Update and Security - Troubleshoot - Other Troubleshooters and select the one for Application Compatibility.
If it uses a AAAA battery then it is required for inking, unlike the Wacom EMR that current is in the screen, the Microsoft (N-Trig) Pen has the power in the pen. One thing you can try is remove the tip of the pen and put it back into the per barrel.