1) If I just junk the alternator and voltage reg harness and wire the alternator to the battery, how does the fuse box get power?
2) What essential functions, if any, does the TCS solenoid perform? Can I live without it?
3) What function does the transmission wire harness perform? Can I live without it?
4) Can I run the vacuum input for the air cleaner from a carb vacuum source or does it have to come from the TCS?
1) yes, get rid of the alternator and voltage regulator. Get rid off the wires except for the heavy Black/Red coming off the factory alternator running to the firewall bulkhead connector. This is the wire that supplies main const 12v power to the ignition/fuse block. Use at least a 4awg wire for the new 1 wire from alternator to battery. Either hook that heavy black/red wire to the alternator post or directly to Batt+. And an fyi your gen light will no longer e functional but you probably knew that when buying the one wire setup.
2) The idle solenoid looks to be of the kind that when power is cut, completely closes the butterflies on the carb to prevent engine run. It can go.
3) The "trans wire" as you say should be the kick down switch. It's a black/yellow drawing power from the wiper connector and sending a black wire to the trans according to the diagram . It's what tells the trans to downshift when you kick it in the ass. Yes keep it.
4) I think you may be referring to the EGR solenoid, not a TCS solenoid. It's an emissions deal and I would just cap it unless you're going for the all original setup which I doubt since you put a holley and other stuff on it. There's no reason for a vacuum line from the carb to the air cleaner, it will just create a vacuum leak. I'm not super familiar with the setup off a '70 gto but typically (if your running a pcv system) one vacuum line off the pcv to the carb/manifold vac. Another vac line from the valve cover to the air cleaner to provide fresh air to crankcase.
* Note when removing the voltage reg wires get rid of them all but be careful with the red wire in position #3
on the reg. It runs to a junction before the firewall where it meets with a heavy wire from the starter and a green wire that takes it to the bulk head. Remove the red volate reg wire from the junction but keep the green wire and wire from starter connected. This also feeds power to the ignition.
Attached is the 2 pages of wiring diagram i referenced... It may not be exact but it will help you track where everything is going...