Guess it depends on if the horse tracks up well, but I probably would as it will more likely stretch when cantering/galloping in the cross country stage. Best to be safe and keep shoes on/prevent cuts.
I would. If a horse scrambles over a fence or stumbles or just needs to get out of a sticky situation it might over reach even if it would not normally. In eventing it is important that the horse sorts itself out and you don't want it to remember pain from a scramble - just your praise for getting you out of it. I'm not a fan of boots in most circumstances - over reach or otherwise. They are so often over used and misused. But I always boot for XC.