"Another question: Can you give me a general summary as to what will happen to the conditions of the snow/trail between now and the time when just a few patches remain?"
The snow will slowly compact and go to a higher water concentration....meaning that it starts to act more like ice, than like snow. The south-facing aspects will go through this faster, then actually melt out first, due to the greater energy going into melting. Also, those areas surrounded by rock will melt faster, as the rock warms up, then continues to release heat later into the evening. Probably the worst place on the trail is at the Cables, where it is north-facing, and quite shielded from sunlight. Water drips down from above, and freezes into ice at night. Probably about the last ice to disappear from the mountain.
"If there was no new snow, would the melting and freezing turn the trail into an ice block until the final melting?"
Pretty much.
"Would there be layers of new snow set on top of slippery ice?"
As the layers melt and refreeze, they bond together. Right after a snowfall, though, your description is correct.
"Are avalanche conditions set up when new snow falls on iced up areas?"
Yes.
