For erase a the holes
Select the inner surfaces, erase them, then erase circle top, and circle down on the surface
You have erase the vertical hole ;)

PS
Take the habit to draw at the same scale than the grid, it's very difficult to manipulate something flying on the faraway free 3D space ;)

Little trick of selection
Select one inner face, you can now make a rectangle box selection, left to right for select all faces inside the box selection : erase them
then make the same with a circle, you can now make a rectangle box selection, left to right for select all circles inside the box selection, erase them
That all maybe 2 seconds