I recommend yoiu ask specific usage questions in the PSE forum.
Moving this discussion to the Photoshop Elements forum.
On your friend's computer, copy the disaster pictures to a thumb drive, external hard drive, or burn to CD or DVD.
Copy the files to your computer. You will now have them in 2 locations!
Open the files in PSE and work on them for your purpose.
And if you want to put your photos on your photoshop.com account, use a web browser and log in that way, then upload the photos and you can sync them back to your computer when you get home, if it still works.
Good luck with the recovery.