Welcome nemeseri,
I've only climbed Shasta as an overnighter, so not sure, but it's my impression that Whitney is easier. People day hike Whitney all the time, but not as much on Shasta.
I think you should forget snowshoes. I recently went up to the cables on Half Dome, and this time of year, snow is well-consolidated, so crampons worked well.
There is a Facebook picture of someone falling through the snow into really deep brush on the Mountaineers' Route approach -- below the Ebersbacher ledges. Take the Ledges if they are clear of snow. There should be lots of tracks through the snow in that area.
As for ropes, the guide services rope up their clients, but I think most independent groups don't. As for the Final 400 or Easy Walk-off, I think I would decide once I got there. If there is still lots of snow on the F400, crampons would make it fun, unless it was slick ice.
