(1) Does it make any difference in performance if I allocate assets of the project to a scratch disc on a new partition on my harddrive?
Yes, it does. You can make the performance worse. Especially if the physical drive is also your system drive as the system partition is very active. But, any drive that has multiple partitions will be degraded if more than one partition is being actively accessed.
Placing the scratch disks and assets on a separate drive away from the system drive will improve your performance. You can assign the locations of the scratch files in edit>preferences>scratch disks. If you use "same as project" and create your projects in a separate folder on the other drive, the scratch files will be placed in subfolders at that same location.
(2) Is it possible to increase the "virtual memory" of PE7 and allocate the swap file to a dedicated partition as it is in Photoshop? This usually increases performance, in my experience.
No. Premiere Elements does not manage its memory usage the same way as Photoshop and there are no memory settings you can change.