weeellll.....
all your proof is saying is that you need 4 lines to make a square, thats not proof that a 1d square is a line.
also, we can see 2d because we veiw it from one more dimension so we have something to compare it to. we cant veiw 1d in reality but you can get the concept by closing your eyes. you cant prove that what you're seeing is in any one shape.
thats also why your proof isnt showing a 1d square. 1d is like looking at a loading bar. there's a connected line that either comes or goes but it doesnt actually have a width, just a length. so in 1d shapes dont exist, just lines.
as for 4d and above, just wikipedia 4th dimension and look at that picture. keep in mind thats supposed to be a solid shape.
but that was a good thought, you seem smart for a 4th grader.