From what I can see it looks like most of the problem is insufficient sanding. Red oak normally doesn't need a wood conditioner. It's woods like maple, pine and alder that are prone to blotch. When you build a box it's a good idea to sand the inside side of the parts prior to assembly. That way you can thoroughly sand it with an electric sander. It should be the only sanding after assembly is if you get glue on the wood and wipe the wood down with a wet cloth. The second picture in post 1 does show a glue stain. If you wash the glue off with a wet rag all you would need to do is a little fine sanding by hand to smooth the wood out where the water raised the grain. It wouldn't leave a spot where the stain wouldn't take. In post 4 the picture at top right shows a lateral line on the center piece of wood. This looks like the mark made by the planer when the board was surfaced. I would sand this line out. The picture at top left looks like you made the bottom too big and the joint didn't pull together at the corner.