My PS3 died with YLOD couple of weeks ago and I got my new PS3 with 160GB hdd today. I also have my old hdd with 500GB including all my game saves. Can I somehow restore my game saves to the new hdd with the older one?
Only if you saved them to the cloud. ie. if you have PS+ membership and have been backing up your saves.
Some saved games can be copied to a USB drive (but not all), but it doesn't sound like you've been doing this.
If I use SATA to USB -cable to connect my old hdd to PS3, can I restore my old gamedata that way (in the same way as regular USB-stick)?
The hard disk in the PS3 is encrypted and can only be read in the PS3 that created the data in the first place. Since that PS3 is not working, there is no way to read the data from that hard disk.
Well, there is one way. Get your old PS3 repaired, either by the 'reflowing' or 'reballing' technique. (Don't send it to Sony though - last I checked their policy was to format all HDDs in PS3s received for repair. Find a 3rd party that will do it.) After this your old PS3 will work again, but don't treat this as a long-term fix - it can be expected to last maybe 3 months. Instead use this opportunity to sign up to PS+ and copy all of your saves to the cloud. Then restore your saves to your new PS3 (you might have to wait 24 hours before you can do this step).
The PS+ part is necessary because a number of saved games are copy protected, and the only way they can be transferred between systems is via the PS+ cloud. Even the backup utility feature won't transfer these files.