I discussed your questions with my friend who restores old "Vintage Tools" and he said:

Lead screws can be restored based on how bad they are nicked. You'll need to get a special file, and follow the threads. You'll need a "double extra slim taper saw file", which is triangular in shape, to do it.

About the slick, that is a sharping done by a previous owner.
It is sharpened this way to help cut the wood. Similar to the way a skew chisel works. It should be only a slight arc.

Corner chisel tip, was made that way to allow you to center the tip in the corner. This tip will grow as you sharpen away each side. Most people try and maintain the tip, to help them put the chisel in the exact corner of a mortise.

Good luck with your project.

Jim Rogers