I'm replacing my range with a separate cooktop and oven. The range is
on a 60 amp 240V circuit.

The new appliances have the following electrical requirements:
Oven: 30 Ampere, 208/240 Volts.
Cooktop: 40 Ampere, 208/240 Volts.

Also the manufacturer recommends a time-delay fuse or circuit breaker
and a separate circuit for each.

Can I use the existing 60 amp circuit for both?

If I need to get two circuits in there, can they share the same
neutral?

Both appliances will be connected wire-to-wire (no plugs). Can I use
the same box for both of them?

Thanks,
Matt
P.S. I'm getting conflicting answers and a wide range of quotes from
electricians, so I wanted to get a better idea.