installing a new cooktop

[Old and In the Way]

2. How many wires on the harness coming from the exhaust fan?

I think they would correspond to the number of speeds that the fan has plus a ground wire (green) and maybe a neutral (white). If there are 5 total, then it would be 3 speeds. You might use a rheostat fan switch - tied to the highest speed lead and make it an adjustable (0-max rpm). Is the wire to the switchbox still in place? If so, I'd try to remount the new switch in the same location.

In rereading your OP, I am confused. Is this a downdraft vent or an exhaust fan and is it located on the cook top or over it? My comment above assumes over the cooktop. If it is part of the cooktop I don't see how the old unit will adapt to the new cooktop. If there is a ffan on the new cooktop, it should have it's own set of wires that would connect to the circuit that your old cooktop used.

On edit: I think MADem is giving good advice if you don't feel comfortable doing electrical work....if you proceed, make sure all power if off to the cooktop/fan circuits before doing anything!