Can you replace a 15 amp fuse with a 30 amp fuse?

Not a good idea. The 15 amp fuse will be protection a #14 wire which is rated for 15 amps maximum capacity. By changing the 15 amp fuse to a 30 amp fuse you would then be allowing 30 amps maximum capacity on a #14 wire. By doubling the load the extra heat generated on the smaller wire could be enough to melt the insulation from the wire and that could cause the wire to short out. If the wire shorts out inside the wall it means the removal of the wall board to replace the wire to restore the circuit to an operational condition. The proper wire sizing for a 30 amp fuse is, #10 copper wire with an insulation rating of 90 degrees C.