The picture in post#4 is of an electronic Ignition distributor.
The gap spec on that one is set to in the range of .008 to .011, and is set using a Non-Magnetic feeler gauge. The gap is not super critical cuz I have seen then as tight as Zero, and all mine will work up to at least .030, the widest I have tried. The gap does not affect the Ignition timing.
For purposes of just getting the engine running, here's what I do;
1) I set the #1 piston to TDC/compression.
2) I install the distributor with the rotor pointing in the general direction of the #1 cylinder. see Note-1
3) I then back the crank up to 10 degrees advanced.
4) then I push the Vcan CW until it hits the firewall
5) then I pull it towards me, CCW little by little until any vane lines up with approximate centerline of the magnetic pole-piece, in the center of the magnet. Snug the D down, plug it in, and install the rotor.
6) mark the OUTSIDE of the D with a vertical line pointing up to the rotor.
7) Install the cap. Whatever tower is above your mark is gonna be your #1. mark it, If no tower lines up, STOP! See note-2
8) install your #1 wire, the one that is gonna go to the #1 Cylinder into the marked tower. then Follow with the rest CW, in the firing order 18436572.
9) now you are ready to fire it up and set the Idle-timing.
Note-1
If the distributor does not drop down into the oil-pump drive, in that position, I just rotate the distributor a lil in either direction until it does. If it is off be very much, then I have to make a decision as to if I want to move it or not. Since it's my car, and my wires are all the same length, I can leave it exactly where-ever it drops in. But if your wires are custom fit/premade, they don't always fit properly, in which case I would pull it out and re-index the driveshaft, as many times as needed to get it in the ballpark of pointing to #1 cylinder. Once it's down, I install the hold down, loosely.
If you had to move the crank, then put #1 piston back to TDC compression.
Note-2
In the unlikely event that no tower lines up, within about 10/20 degrees, something is wrong. Recheck your work. Make sure the rotor advances on it's springs and snaps back to it's parked spot. If your work is good then the distributor cannot be used as it is, because the driveshaft is out of sync with the reluctor.
The Reluctor has two slots machined into it, one for CW rotation and the other for CCW. they are marked. Remove the rotor, and Find the slot. follow it up to the top of the reluctor, where the slot comes to the top face of the reluctor. There you should see the arrow pointing in the direction that your installed distributor rotates. If it is not pointing in the Correct direction, Just pull it off and reinstall it on the other slot, making sure it goes all the way down.
That reluctor is a light press-fit, and sometimes you have to pry it up, and sometimes you have to tap it back down. Then try again.
But
if a tower still does not line up, the D is made wrong and it will have to be modified, or thrown away.
Note-3
What you call a "nipple", I think you mean, the vane. There is one for every cylinder so for a V8 that would total 8. and
The thing you call a "circular collar" is the reluctor and the vanes are part of it; and
the stationary "Doodad" is the magnetic pick-up, usually just called the pick-up.
In the center of the pick-up is the pole piece.
As to the lines (notches) on the top of the reluctor, IDK what those are for.
The Pick-up is just a tiny electro-magnet. Every time a vane passes by the pole-piece, it sends a tiny voltage spike back to the ECU, which amps it up and translates it into something that the coil then uses to fire the sparkplug.
As always, Happy HotRodding.