Get your sandpaper out and start over.
Brushing shellac on a table that big takes AC/DC sized balls. It could be the stain lifting or it could just be lap marks from the shellac. The stuff dries fast and if you are using an amber shellac you will get dark lap marks.
I'd spray it. You can also add a small amount of turpentine to shellac (1 tsp per 4oz of shellac) to slow down the dry time if you are brushing.
I don't want to criticize your technique but your brush strokes look awfully short to me. Maybe you need a better brush?
Coming back to this question. This is what I was thinking of doing. I was going to route out a trench in the top piece to accept the cross piece that connects the legs. On the legs themselves I was thinking about doing some sort of dowel pins, if it is even necessary. Domino's would be good, but I don't know anyone with a machine.