Middle Palisade is a classic third class climb. It is just getting from the snow onto the rock that is the problem, as the old ice field/glacier has melted away from the point where was an easy hop across the crack onto the mountain. But now that it has melted far away, there is a steep wall at the base to climb. Once you get above the ice field, the climbing is fun third class.
The Final 400 with ice can be done in May -- a number of climbers do it. Guide services always rope their clients on that section, but private groups tend to do it without. In May, you will need ice axe and crampons. The bad place in May, if you choose to do the traverse, is the westward traverse just west of the Notch. It is steepest there, with no end to the steep descent below. Doing the Final 400 would be safer if that traverse is too icy.
