1- Cone curvature is important in that both the spot on the cones that the balls contact needs to be between the edges (within the curved surface) as well as the curve is not too tight for the hub's ball diameters. So the balls need to fit on the curve close to it's center and not touch at two points (if the balls were to large for the curve). Front hubs that use 3/8" (9.5mm) axles can have either 3/16" or 1/4" ball diameters, their coves are shaped for the stock ball diameter and ball count.

2- Every FW or cassette I've seen has a center hole with enough clearance for 3/8" or 10mm axles. It's the hub shell/free hub body that really controls the cogs mounting. Now the axle does need the correct amount of extension/spacers so the cogs don't hit the inside of the drop out/seat stay or sit so far away the the rear der can't swing far enough in to the large cog.

3- Yes, Cone OD needs to fit through the hub shell's dust cap. If the cone has a press on dust cap then this needs to fit within the shell's spot for it. The cone's length needs to be enough to have the wrench flats be outside the dust cap, or doing bearing adjustments and cone/lock nut tightening gets REAL frustrating. The easiest way to assure all these issues is to get an axle with the same diameter and thread pitch. Then all the cones, spacers and lock nuts can just transfer over. BTW many classic front nutted/solid axles are a smaller diameter then the QR version. Many rear axles have the same diameter for both. Any changes to the cones or lock nuts will likely mean that the spacers will need playing with. So getting extra 1mm spacers can save a return to the shop. bring in all your parts when you go so their trained eyes can help reduce the challenges by providing the best fits the first time. Andy.