I think everything you look at downstream of the regulator should be DC voltage only. The presence of AC (I think) indicates a failure of the rectifier.
Pull up the
service manual (there is a good Clymer one) at this link:
http://www.oscarmayer.net/atc/manuals/ .
You are correct, the lighting coil powers the headlamp and taillamp, the charging coil provides the power to recharge the battery. The CDI uses the regulated 12V power, not the AC directly from the magneto. There are connection to the mag, but these are the triggers to fire the spark plug, rather than power feeds to the CDI.
Chapter 7 of the Clymer manual has a bunch of electrical checks. For the lighting coil, it gives you the voltage levels you should see at different RPM's. They say the headlight voltage should be: greater than 11.3 at 3000 RPM, and less than 18 volts at 8000 RPM. (basically it should be between 11.3 and 18).
Also, they give the resistance spec on the coils, which can be used as a basic check of the health of the coil. The lighting coil is the yellow with red stripe wire and the black wire. The lighting coil is 0.34 ohms +/- 10%. The charging coil is the white wire and black wire (black must be common to both). The charging coil should be 0.4 ohms +/- 10%. I find measuring this low of a resistance is tough to do accurately unless you have a good meter. Also, the numbers given in the manual are at room temp. If you are measuring this outside in the cold, the values will be lower.
With regards to the charging, this could be limited by your battery. If your battery isn't topped off on charge, then your charging system won't be able to get the voltage up right away (eventually it will if it is charging). Another way is to put an ammeter inline between the battery and the battery line to the charging system (NOT on the heavy gauge lead that feeds the starter, you'll blow the fuse to your meter when you crank the motor). The book says you should have at least 0.7 amps at 3000 RPM.
Sorry for so much info. This is all just from the manual, so grab that on-line at the link and take it slow from the top.