Hi rustopha, welcome to the HP Support Forums.
The DVD drive spinning means something is trying to access the drive. The noise could be caused by excess dust in the drive, or wear and tear on the drive.
Do you have an antivirus software installed? If so, see if it might be trying to scan the drive. If you have 'File Explorer' opened, it will scan the drive to see the contents, or header info. Do you have shortcuts to the DVD drive anywhere? Do you have DVD burning software installed?
There are several updates for such HP provided software under "Software - Multimedia section for Windows 8.1". Manually install the ones you need: HP Pavilion 15-n096ea Notebook PC Drivers
The TouchPad could be lagging if the drivers are corrupt, or not up to date. Try to uninstall the TouchPad software, and then install the update: Synaptics TouchPad Driver
If that doesn't help, try disabling gestures, or adjusting the various sensitivities. This document has the instructions: Using and Troubleshooting the TouchPad (Windows 8)
Try uninstalling "The HP Support Assistant" and reinstalling this version of: The HP Support Assistant
Check for updates after reinstalling, and make a list of the specific updates that are problematic.
I hope this helps, let me know how everything goes.