Charging problems

You are on the right track. In addition to the tests you already did, test each of the yellow leads to engine ground. There should be no continuity to ground, but I suspect you may find these leads grounded.  Start with the ohm or kilo-ohm scale, that should be adequate for this test.    

You should be seeing 10v+ AC at idle and 30v+ AC at high rpm On the Yellow wires when they are not under load. (Disconnected).
The most common problem is bad connections.
Pull the connector Off the regulator and look closely at both halves.
Reconnect the regulator.

Engine OFF

C, R, and B+ to Ground should equal the DC battery voltage. (~12.6)
Measure the voltage on the Regulator Pins, Not the Connector Pins.
Most importantly, they should all be the SAME.


Engine ON

G to G  should be more than 15V AC.
C, R, and B+ to Ground should be slightly more than the DC battery voltage and the SAME. (~13v+)

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Most meters do not do very well below 5 ohms. You're just asking too much.
You will need a 4-lead Mili-Ohm Meter to measure that accurately.
Notice that when touching the probe leads together, the reading is often not zero.

Well.  After much diagnosing, buying a new multimeter, head scratching, reading advice,(thanks all, by the way), I was struck with a shot of common sense and checked the fuses, DUUHHHH!!!

Problem solved!?

Caution: Fuses usually "blow" for a reason. Sure replace and see what happens BUT if it blows again, you have a deeper problem.

What circuit is your fuse on?