[wdfifteen]

The "crack" in the water damaged area is the glue joint between the boards that were glued together to make the table-top. The glue may have been softened by the moisture, or the wood expanded when it got wet, then shrank when it dried, pulling the joint apart mechanically - or both. The loss of the connection between the boards on either side of the crack needs to be addressed. I would test the strength of the joint by gently flexing the table-top to see if it comes apart. If it does, the edges need to be straightened by running them through a jointer, then re-glued. If it's still strong, you can go ahead and fill the crack.

This video shows how to deal with the black stain at about the 7:15 mark.