Your #3 is the hot from the regulator. Yes it screws into the brass nut in the brush holder.
If the battery voltage drops below the 14.5 preset the regulator sends battery voltage to the brush on that green wire through the brushes and rotor to ground, this energizes the rotor to create the magnetism to excite the stator.
Now the battery voltage is grounding somewhere. Have you checked the rotor for continuity? The rotor should have 5 ohms from slip ring to slip ring and infinity to ground. If your rotor is shorting to ground , that can blow the fuse.
If the bakelite is cracked or broken it may short to ground.
Oh just had a thought, the brushes are different. The hot brush, the one #3 goes into the metal holder is the short one, it just goes from under the screw, up the side of the holder and over the brush.
The ground brush has that plus it goes down the other side under the #2 screw then over under the #1 screw. So it's held by #'s 1,2and 4. If you installed the brushes opposite, you will have the long brush under #'s 1,3,4 instead of under #'s 1,2,4. This will send power to ground on screw #'s 1 and 4.