Now we see the pictures. It is unlikely the cracks can be closed. Those look to be separate boards and over they years they have shrunk. Soaking may get some water in the outer cells but not for long and likely never to the inner cells. That is the nature of wood.
As for the top. Likely that was originally steam bend. Could it be again? Perhaps, but I'd take a hard look at the whole project. I'd think this one takes considerable skill, money and time to make new again. You didn't tell us your skill level or experience. So it is hard to know where to begin.
Dave Hawksford is our resident refinishing guy. Hopefully he will pop in with some thoughts.