Could the UN be an actual government of territory?

Wherever two countries have a border that is associated with some problems (not necessarily military conflict between the two countries), the countries could both agree to give a strip of land along the border to the UN. The amount of land given to the UN might depend on how much land a given country can spare and how serious the border problems are. Then the UN would control territory and it could have people living permanently under its jurisdiction.

In this case, the UN would simply have to control its borders and ordinary member nations would not be in direct conflict with each other over borders. A given ordinary member nation of the UN might have borders with the special UN territory, but it wouldn't have borders with other ordinary member nations of the UN.

The UN is probably too corrupt to handle any kind of responsibility like that. (Remembe the "Oil for Food" program?)

could participate in UN elections that decided who controls the UN. I mean ordinary citizens, not governments.

I don't think we could trust the results of those elections.

nation deliberately engaged in fraud involving the process of citizens voting in UN elections in that nation, then it might be a good idea to either put the government of that nation on some kind of probationary status or throw it out of the UN.