My MacMini keep booting after I update YOSEMITE

Hi there

My mac mini keep booting after I update new os

the last update my photoshop had crashed every single time i open it

then 2 days ago...I update the new os

then yesterday when i working with my mac, it suddenly pop to reboot

and the logo on the loading screen looks wired

and whenever it get to 1/3 of the loading, it becomes white screen and reboot again, I have never get a chance to get into desktop.😢

then i tried a hardware test, there seem nothing show

so...i decide to make a recovery

they screen looks like this below

And the worse part is I dun have a chance to backup or save my file in the mac.😢

I was wondering, is there anyway i read my HDD and get the file first?

P.S. and also this happen with my Macbook Air too, but luckily it boot back to desktop?

so is it the new OS crashing my hardware?