The MR is Class 2-3. You will encounter precisely 0 5th class unless you're looking for the hard way, or the wrong way.
IF you're comfortable with tread, the final 400' is a cake-walk. Many people rope up for more mental security. In March you'll be running with spikes, so a running belay with your partner might be advisable, but if you have solid footwork and point-placement, you won't have too much issue. Twin ropes will likely be helpful if there is a cornice at the top though (for like maybe 6m).
I'm no snow mountaineer, but both the MR and MWMT deal with narrow gullies below broad and steep N. Faces. You'll face some danger going up Whitney's E. Chute, but it gets the most sun so it should be pretty well consolidated in March.
We'll have to see how the snow season ends.
As far as shoes, I can't say.
