Is Everything capturing the mouse movement for scrolling the result list? -you can use the middle mouse button to scroll the result list in Everything. While scrolling the result list the mouse cursor will appear still.
Might be a high CPU usage issue? -If you leave the Task Manager open (Ctrl + Shift + ESC) Does Everything have high CPU when the mouse is frozen?
It could also be Disk IO, you could try watching Everything's IO with the Windows Resource Monitor.
It seems odd you can still use the keyboard, but not the mouse..
When the mouse freezes, could you try terminating any Everything.exe processes in the task manager with the keyboard, does the mouse unfreeze when you terminate Everything?