The long straight crack in the floor tile is consistent with tiling over a concrete control joint without using an uncoupling membrane. No fixing that now without removing the tile. Expect it to get worse please; replacement tile will crack in the same place.

We are hoping to replace the tile and don't want to see the same thing again. the tile is on a wood floor with the underlayment shown .Is that the problem. Floor is pretty old.

Wood or concrete, the theory is the same. You're getting movement in the underlayment that's causing the cracks. Stiffen the floor and you'll be fine.