I have an older home that has a 100 amp (screw in type) fuse panel with a 60 amp fused main and a range pull-out that is not being utilized. My question concerns the range pull out which is currently not being used. I plan to add a sub panel from that range side with 2-30amp 220v breakers. Can the range side also have 60 amp fuses or does it have to have 40 amp fuses to add to the 100 amps of the fuse box? How does this work?

The "range" fuses can be up to 60A. The actual sum of the fuses or breakers is irrelevant.