How close can a gas heating systems shut off switch be to the gas shut off valve? Also, the heating systems shut off switch included a screw-in type fuse should there be any concerns? Observed a box of fuses which could indicate the fuse blows often.
I see no issue.
No proximity rule I am aware of even if not liking it.
No problem with the location as long as it does not hinder the closing of the valve. The fuse is a 15 amp and the amp draw of a fractional hp motor is much less than 15 amps and should not be blowing fuses. Did you check to see if the furnace circuit was dedicated as that is a requirement.
Fuses typically come in boxes of four. How many were missing from the box? One? Okay, it is installed. Two? Okay, one blew and it was replaced. Three? Perhaps an issue to look into. Four? Who keeps empty fuse boxes laying around? 
If it appears that the fuse regular blows, recommend that TD (time delay) fuses be used.
At start-up on some furnaces, instantaneous amperage spikes above 15 amps. In my area, the techs (??) or homeowner will insert a 20A fuse instead of the 15A to solve the problem of nuisance blowing of the 15A! The TD fuse will allow the instantaneous spike and continue to protect at the 15A level.
Why not just install a 100 amp fuse and be done with it:twisted: