What if Bethesda fixes something that they fixed but in a different way, could this in the future destroy my save or something unforeseen?
Nope. They get frequently updated. When the 1.9 patch came out they updated the patches only a day later I think. Besides Bethesda doesnt even touch most things that get fixed by the unofficial ones. These guy know what they are doing and have much experience.
You should get the Skyrim Nexus and look the patches up and read the changelogs. You will probably find bugs in there that you have already encountered.
I have
- Dawnguard
- Hearthfire
- Dragonborn
Should I then download the unofficial patch for Skyrim first, then go from top to buttom or something? *erh*

Doenst matter. They are independent from each other.