Okay the question is, that if i have had the original game, without any dlc, would i still have access to my old saves if i just buy the skyrim legendary edition? A completely different disc?

Yes, your saves will work just fine.

All the DLC is installed from a second disc onto your hard drive, but you still play from a traditional "Skyrim only" disc.
You could even use your old Skyrim disc if you want to.

yes, you can load your previous save and the game will do everything else

So does the legendary edition give you two discs? One that is the original skyrim disc and a second disc that contains all the dlc?