1
If there is currently a version of Windows installed on your laptop, please check to see if your PC is producing any minidump files, I will check those to see if they provide any insight into a potential cause of the system crashes.
Please do not upload a very large Memory.dmp file.
Open Windows File Explorer.
Navigate to C:\Windows\Minidump
Copy any minidump files onto your Desktop, then zip those up.
Upload the zip file to the Cloud (OneDrive... etc.), then choose to share those and get a share link.
Then post the link here to the zip file, so I can take a look for you.
2
For the problems installing Windows 11, either the Windows 11 USB you were using is corrupt, or because of all the problems you indicate, there may be an underlying hardware fault.
The best option is to create a new bootable Windows 11 USB on a different USB flash drive using the official Media Creation Tool.
Then reset BIOS to defaults to undo any changes you previously made in BIOS.
Insert the USB into your laptop and start it.
On the HP logo screen, repeatedly press Esc, then on the next menu, press F9 to get the temporary boot menu and select the USB as the boot option to begin the installation.