Circ arrest - necessary for anastamosis of the branches of the arch, because you can't flow from the aorta (where the normal cannulation site is) to the head if they need to fix that connection. You could still flow blood to the head through the right subclavian and clamp the brachialcephalic trunk (innominate artery), as antegrade flow, or through the jugular veins as retrograde flow (less common)
Frozen elephant trunk - repair technique for extensive dissections that goes from ascending to descending. After you repair the ascending, you leave a graft hanging in the true lumen of the dissected descending aorta for a later 2nd stage repair. Sometimes the 2nd stage can be done endovascularly without a second surgery, although only a few centers do this.
Two staged repair - when referring to aorta reconstruction, it's a more broad term. Usually the ascending dissection causes the most mortality and can involve very extensive pump runs. So the idea is let the pt recover from that and fix the less mortality inducing descending dissection later. The frozen elephant trunk is one type of two stage repair.
Evidence based anesthesia - the only evidence proven reduction in mortality is the temperature of blood while on circ arrest. Many people cool to 19c or colder. There are adjuncts such as high dose glucocorticoids, antegrade/retrograde cerebral perfusion, ice around the head, and others that are debated and very center dependent.
Hope this helps clarifying the confusion.
I knew a resident who used to say understood in the place of "okay". I called him understood because I'm a huge troll.