Select all of the geometry by triple clicking on it with the Select tool, right click on it and choose Soften/Smooth. Also correct the faces orientation as I directed before. Select all of the geometry of the peg as above, right click and choose Reverse Faces. You want white faces out, not blue.
You should select and delete the face skinning the hole (it shows blue in your latest screen shot) and before you let the peg touch the block, make sure you make each one a group or component. Otherwise they’ll stick together and you won’t be able to get them apart.
Ol’ Dan’l Webster wrote a thick book he called the Dictionary. I think most kids in the recent past might have only used one as a booster seat when they were small.