No fuse box, everything is fused separately. Yes, switch has (2) run and (1) start. 1st run is constant and 2nd is only hot in run not during start (if that makes sense).
Something like this?
To your alternator charging question, that part is easy.
Output stud to battery with fusible link is correct. Every wire attached to the battery positive should have a fusible link except the ones for the starter.
Power to alternator field can come from the Run position. (blue wire)
Measurement of system voltage by the regulator should also come from the run position.
The field's ground is controlled by the regulator (green wire).
On the diagram I wasn't sure how you plan to power the equipment. It would be best to get the power from as close to the alternator as possible.
That does mean during starting power will have to go through the fusible link to the alternator stud first, but that's the advantage of a fusible link over a fuse for the charging wire.
Not quite sure how your temp switch will supply power in the start position so I left the remnants of the OEM system in the diagram although disconnected.